@prefix dbo: . @prefix dbr: . dbr:All-pass_filter dbo:wikiPageWikiLink dbr:Complex_plane . dbr:Imaginary_number dbo:wikiPageWikiLink dbr:Complex_plane . dbr:Zeros_and_poles dbo:wikiPageWikiLink dbr:Complex_plane . dbr:Geometric_series dbo:wikiPageWikiLink dbr:Complex_plane . dbr:Stirling_numbers_of_the_first_kind dbo:wikiPageWikiLink dbr:Complex_plane . dbr:Exponential_function dbo:wikiPageWikiLink dbr:Complex_plane . dbr:Entire_function dbo:wikiPageWikiLink dbr:Complex_plane . dbr:Reflection_formula dbo:wikiPageWikiLink dbr:Complex_plane . dbr:Harmonic_number dbo:wikiPageWikiLink dbr:Complex_plane . dbr:Natural_logarithm dbo:wikiPageWikiLink dbr:Complex_plane . dbr:Trigonometric_functions dbo:wikiPageWikiLink dbr:Complex_plane . @prefix rdf: . @prefix yago: . dbr:Complex_plane rdf:type yago:Number113582013 , yago:DefiniteQuantity113576101 , yago:WikicatComplexNumbers . @prefix owl: . dbr:Complex_plane rdf:type owl:Thing , yago:Abstraction100002137 , yago:ComplexNumber113729428 , yago:Measure100033615 . @prefix rdfs: . dbr:Complex_plane rdfs:label "P\u0142aszczyzna zespolona"@pl , "Plano complexo"@pt , "\u041A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0430\u044F \u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u044C"@ru , "Plano complejo"@es , "Piano complesso"@it , "\uBCF5\uC18C\uD3C9\uBA74"@ko , "Pla complex"@ca , "\u041A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0430 \u043F\u043B\u043E\u0449\u0438\u043D\u0430"@uk , "Complexe vlak"@nl , "\u0645\u0633\u062A\u0648\u0649 \u0639\u0642\u062F\u064A"@ar , "Plano konplexu"@eu , "\u8907\u7D20\u5E73\u9762"@ja , "Gau\u00DFsche Zahlenebene"@de , "Komplex vektor"@sv , "Kompleksa ebeno"@eo , "Bidang kompleks"@in , "Plan complexe"@fr , "Complex plane"@en , "\u590D\u5E73\u9762"@zh , "Komplexn\u00ED rovina"@cs , "\u039C\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03CC \u03B5\u03C0\u03AF\u03C0\u03B5\u03B4\u03BF"@el ; rdfs:comment "P\u0142aszczyzna zespolona, p\u0142aszczyzna Gaussa \u2013 geometryczny model cia\u0142a liczb zespolonych P\u0142aszczyzna pe\u0142ni w nim w stosunku do liczb zespolonych rol\u0119 analogiczn\u0105 do roli, kt\u00F3r\u0105 pe\u0142ni wzgl\u0119dem cia\u0142a liczb rzeczywistych. gdzie Przyporz\u0105dkowanie to jest r\u00F3\u017Cnowarto\u015Bciowe i obrazem p\u0142aszczyzny jest w nim zbi\u00F3r wszystkich liczb zespolonych. Zatem oba zbiory mo\u017Cna uto\u017Csami\u0107. W zwi\u0105zku z tym o\u015B odci\u0119tych nazywa si\u0119 osi\u0105 rzeczywist\u0105, a o\u015B rz\u0119dnych \u2013 osi\u0105 urojon\u0105 (od pierwiastka kwadratowego z minus jedynki, nazywanego pierwiastkiem urojonym). Zapisujemy to nast\u0119puj\u0105co: Wtedy Z definicji tych wynika, \u017Ce:"@pl , "En matem\u00E0tiques, el pla complex \u00E9s una forma de visualitzar l'espai dels nombres complexos. Pot entendre's com un pla cartesi\u00E0 modificat, en el que la part real est\u00E0 representada a l'eix x i la part imagin\u00E0ria a l'eix y. L'eix x tamb\u00E9 rep el nom d'eix real i l'eix y el d'eix imaginari. El pla complex tamb\u00E9 s'anomena Pla d'Argand, ja que s'utilitza en els diagrames d'Argand. Aquests porten el nom de Jean-Robert Argand (1768-1822). Els diagrames d'Argand s'usen sovint per representar les posicions dels pols i zeros d'una funci\u00F3 en el pla complex."@ca , "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u8907\u7D20\u5E73\u9762\uFF08\u3075\u304F\u305D\u3078\u3044\u3081\u3093\u3001\u72EC: Komplexe Zahlenebene, \u82F1: complex plane\uFF09\u3042\u308B\u3044\u306F\u6570\u5E73\u9762\uFF08\u3059\u3046\u3078\u3044\u3081\u3093\u3001\u72EC: Zahlenebene\uFF09\u3001z-\u5E73\u9762\u3068\u306F\u3001\u8907\u7D20\u6570 z = x + iy \u3092\u76F4\u4EA4\u5EA7\u6A19 (x, y) \u306B\u5BFE\u5FDC\u3055\u305B\u305F\u76F4\u4EA4\u5EA7\u6A19\u5E73\u9762\u306E\u3053\u3068\u3067\u3042\u308B\u3002\u8907\u7D20\u6570\u306E\u5B9F\u90E8\u3092\u8868\u3059\u8EF8\u3092\u5B9F\u8EF8 (real axis)\uFF08\u5B9F\u6570\u76F4\u7DDA\uFF09\u3001\u865A\u90E8\u3092\u8868\u3059\u8EF8\u3092\u865A\u8EF8 (imaginary axis) \u3068\u3044\u3046\u3002 1811\u5E74\u9803\u306B\u30AC\u30A6\u30B9\u306B\u3088\u3063\u3066\u5C0E\u5165\u3055\u308C\u305F\u305F\u3081\u3001\u30AC\u30A6\u30B9\u5E73\u9762 (Gaussian plane) \u3068\u3082\u547C\u3070\u308C\u308B\u3002\u4E00\u65B9\u3001\u305D\u308C\u306B\u5148\u7ACB\u30641806\u5E74\u306B \u3082\u540C\u69D8\u306E\u624B\u6CD5\u3092\u7528\u3044\u305F\u305F\u3081\u3001\u30A2\u30EB\u30AC\u30F3\u56F3 (Argand Diagram) \u3068\u3082\u547C\u3070\u308C\u3066\u3044\u308B\u3002\u3055\u3089\u306B\u3001\u305D\u308C\u4EE5\u524D\u306E1797\u5E74\u306E \u306E\u66F8\u7C21\u306B\u3082\u767B\u5834\u3057\u3066\u3044\u308B\u3002\u3053\u306E\u3088\u3046\u306B\u8907\u7D20\u6570\u306E\u5E7E\u4F55\u7684\u8868\u793A\u306F\u30AC\u30A6\u30B9\u4EE5\u524D\u306B\u3082\u77E5\u3089\u308C\u3066\u3044\u305F\u304C\u3001\u4ECA\u65E5\u7528\u3044\u3089\u308C\u3066\u3044\u308B\u3088\u3046\u306A\u5F62\u5F0F\u3067\u8907\u7D20\u5E73\u9762\u3092\u8AD6\u3058\u305F\u306E\u306F\u30AC\u30A6\u30B9\u3067\u3042\u308B\u3002\u4E09\u8005\u306E\u540D\u524D\u3092\u3068\u3063\u3066\u30AC\u30A6\u30B9\u30FB\u30A2\u30EB\u30AC\u30F3\u5E73\u9762\u3001\u30AC\u30A6\u30B9\u30FB\u30A6\u30A7\u30C3\u30BB\u30EB\u5E73\u9762\u306A\u3069\u3068\u3082\u8A00\u308F\u308C\u308B\u3002"@ja , "\u6570\u5B66\u4E2D\uFF0C\u590D\u5E73\u9762\uFF08\u82F1\u8A9E\uFF1AComplex plane\uFF09\u662F\u7528\u6C34\u5E73\u7684\u5B9E\u8F74\u4E0E\u5782\u76F4\u7684\u865A\u8F74\u5EFA\u7ACB\u8D77\u6765\u7684\u8907\u6578\u7684\u51E0\u4F55\u8868\u793A\u3002\u5B83\u53EF\u89C6\u4E3A\u4E00\u4E2A\u5177\u6709\u7279\u5B9A\u4EE3\u6570\u7ED3\u6784\u7B1B\u5361\u513F\u5E73\u9762\uFF08\u5B9E\u5E73\u9762\uFF09\uFF0C\u4E00\u4E2A\u590D\u6570\u7684\u5B9E\u90E8\u7528\u6CBF\u7740 x-\u8F74\u7684\u4F4D\u79FB\u8868\u793A\uFF0C\u865A\u90E8\u7528\u6CBF\u7740 y-\u8F74\u7684\u4F4D\u79FB\u8868\u793A\u3002 \u590D\u5E73\u9762\u6709\u65F6\u4E5F\u53EB\u505A\u963F\u5C14\u5188\u5E73\u9762\uFF0C\u56E0\u4E3A\u5B83\u7528\u4E8E\u963F\u5C14\u5188\u56FE\u4E2D\u3002\u8FD9\u662F\u4EE5\u8BA9-\u7F57\u8D1D\u5C14\u00B7\u963F\u5C14\u5188\uFF081768-1822\uFF09\u547D\u540D\u7684\uFF0C\u5C3D\u7BA1\u5B83\u4EEC\u6700\u5148\u662F\u632A\u5A01-\u4E39\u9EA6\u571F\u5730\u6D4B\u91CF\u5458\u548C\u6570\u5B66\u5BB6\u5361\u65AF\u5E15\u5C14\u00B7\u97E6\u585E\u5C14\uFF081745-1818\uFF09\u53D9\u8FF0\u7684\u3002\u963F\u5C14\u5188\u56FE\u7ECF\u5E38\u7528\u6765\u6807\u793A\u590D\u5E73\u9762\u4E0A\u51FD\u6570\u7684\u6781\u70B9\u4E0E\u96F6\u70B9\u7684\u4F4D\u7F6E\u3002 \u590D\u5E73\u9762\u7684\u60F3\u6CD5\u63D0\u4F9B\u4E86\u4E00\u4E2A\u590D\u6570\u7684\u51E0\u4F55\u89E3\u91CA\u3002\u5728\u52A0\u6CD5\u4E0B\uFF0C\u5B83\u4EEC\u50CF\u5411\u91CF\u4E00\u6837\u76F8\u52A0\uFF1B\u4E24\u4E2A\u590D\u6570\u7684\u4E58\u6CD5\u5728\u6781\u5750\u6807\u4E0B\u7684\u8868\u793A\u6700\u7B80\u5355\u2014\u2014\u4E58\u79EF\u7684\u957F\u5EA6\u6216\u6A21\u957F\u662F\u4E24\u4E2A\u7EDD\u5BF9\u503C\u6216\u6A21\u957F\u7684\u4E58\u79EF\uFF0C\u4E58\u79EF\u7684\u89D2\u5EA6\u6216\u8F90\u89D2\u662F\u4E24\u4E2A\u89D2\u5EA6\u6216\u8F90\u89D2\u7684\u548C\u3002\u7279\u522B\u5730\uFF0C\u7528\u4E00\u4E2A\u6A21\u957F\u4E3A 1 \u7684\u590D\u6570\u76F8\u4E58\u5373\u4E3A\u4E00\u4E2A\u65CB\u8F6C\u3002"@zh , "Komplexn\u00ED rovina (\u010Dasto t\u00E9\u017E Gaussova rovina) je v matematice zp\u016Fsob zobrazen\u00ED komplexn\u00EDch \u010D\u00EDsel. Ve frankofonn\u00ED literatu\u0159e b\u00FDv\u00E1 n\u011Bkdy ozna\u010Dov\u00E1na jako Argandova rovina, Cauchyho rovina nebo Argand\u016Fv diagram. Na osu x se vyn\u00E1\u0161\u00ED re\u00E1ln\u00E1 \u010D\u00E1st komplexn\u00EDho \u010D\u00EDsla z, tzn. , a proto je tato osa ozna\u010Dov\u00E1na jako re\u00E1ln\u00E1. Na osu y se vyn\u00E1\u0161\u00ED imagin\u00E1rn\u00ED \u010D\u00E1st komplexn\u00EDho \u010D\u00EDsla z, tzn. , a proto je tato osa ozna\u010Dov\u00E1na jako imagin\u00E1rn\u00ED. Komplexn\u00ED rovinu, do n\u00ED\u017E zahrnujeme i nevlastn\u00ED bod , ozna\u010Dujeme jako roz\u0161\u00ED\u0159enou rovinu (komplexn\u00EDch \u010D\u00EDsel). Tato z\u00FApln\u011Bn\u00E1 komplexn\u00ED \u010D\u00EDsla v\u0161ak n\u00E1zorn\u011Bji zobrazuje Riemannova koule."@cs , "\u041A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0430 \u043F\u043B\u043E\u0449\u0438\u043D\u0430 \u2014 \u043C\u043D\u043E\u0436\u0438\u043D\u0430 \u0432\u043F\u043E\u0440\u044F\u0434\u043A\u043E\u0432\u0430\u043D\u0438\u0445 \u043F\u0430\u0440 , \u0434\u0435 . \u0417\u0430\u0437\u0432\u0438\u0447\u0430\u0439 \u043F\u0440\u043E\u0432\u043E\u0434\u0438\u0442\u044C\u0441\u044F \u0443\u0442\u043E\u0442\u043E\u0436\u043D\u0435\u043D\u043D\u044F \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0457 \u043F\u043B\u043E\u0449\u0438\u043D\u0438 \u0456 \u043F\u043E\u043B\u044F \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0438\u0445 \u0447\u0438\u0441\u0435\u043B \u0437\u0430 \u043F\u0440\u0438\u043D\u0446\u0438\u043F\u043E\u043C . \u0426\u0435 \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u0454 \u0432\u0432\u0435\u0441\u0442\u0438 \u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0456 \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u0457 \u043D\u0430 \u043F\u043B\u043E\u0449\u0438\u043D\u0456 . \u0420\u043E\u0437\u0433\u043B\u044F\u043D\u0435\u043C\u043E \u0442\u043E\u043F\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u0456 \u0432\u043B\u0430\u0441\u0442\u0438\u0432\u043E\u0441\u0442\u0456 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0457 \u043F\u043B\u043E\u0449\u0438\u043D\u0438 \u0456 \u043D\u0435 \u0431\u0443\u0434\u0435\u043C\u043E \u043F\u0440\u043E\u0432\u043E\u0434\u0438\u0442\u0438 \u0440\u0456\u0437\u043D\u0438\u0446\u0456 \u043C\u0456\u0436 \u043F\u0430\u0440\u043E\u044E \u0456 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0438\u043C \u0447\u0438\u0441\u043B\u043E\u043C . \u041A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0443 \u043F\u043B\u043E\u0449\u0438\u043D\u0443 \u0456\u043D\u043E\u0434\u0456 \u043D\u0430\u0437\u0438\u0432\u0430\u044E\u0442\u044C \u043F\u043B\u043E\u0449\u0438\u043D\u043E\u044E \u0410\u0440\u0433\u0430\u043D\u0434\u0430, \u0430 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0456 \u043D\u0430 \u0446\u0456\u0439 \u043F\u043B\u043E\u0449\u0438\u043D\u0456 \u0434\u0456\u0430\u0433\u0440\u0430\u043C\u0430\u043C\u0438 \u0410\u0440\u0433\u0430\u043D\u0434\u0430. \u0412\u043E\u043D\u0438 \u043D\u0435\u0437\u0432\u0430\u043D\u0456 \u0432 \u0447\u0435\u0441\u0442\u044C (1768\u20141822), \u0445\u043E\u0447\u0430 \u0432\u043F\u0435\u0440\u0448\u0435 \u0457\u0445 \u043E\u043F\u0438\u0441\u0430\u0432 \u043D\u043E\u0440\u0432\u0435\u0437\u044C\u043A\u043E-\u0434\u0430\u0442\u0441\u044C\u043A\u0438\u0439 \u0437\u0435\u043C\u043B\u0435\u0432\u043F\u043E\u0440\u044F\u0434\u043D\u0438\u043A \u0456 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A (1745\u20141818)."@uk , "\u03A3\u03C4\u03B1 \u039C\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AC, \u03C4\u03BF \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03CC \u03B5\u03C0\u03AF\u03C0\u03B5\u03B4\u03BF \u03AE z-\u03B5\u03C0\u03AF\u03C0\u03B5\u03B4\u03BF \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BC\u03AF\u03B1 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03B9\u03BA\u03AE \u03B1\u03BD\u03B1\u03C0\u03B1\u03C1\u03AC\u03C3\u03C4\u03B1\u03C3\u03B7 \u03C4\u03C9\u03BD \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03CE\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD ,\u03C4\u03BF \u03BF\u03C0\u03BF\u03AF\u03BF \u03B8\u03B5\u03C3\u03C0\u03AF\u03C3\u03C4\u03B7\u03BA\u03B5 \u03B1\u03C0\u03CC \u03C4\u03BF \u03C0\u03C1\u03B1\u03B3\u03BC\u03B1\u03C4\u03B9\u03BA\u03CC \u03AC\u03BE\u03BF\u03BD\u03B1 \u03BA\u03B1\u03B9 \u03C4\u03BF \u03BF\u03C1\u03B8\u03BF\u03B3\u03CE\u03BD\u03B9\u03BF \u03C6\u03B1\u03BD\u03C4\u03B1\u03C3\u03C4\u03B9\u03BA\u03CC \u03AC\u03BE\u03BF\u03BD\u03B1. \u0391\u03C5\u03C4\u03CC \u03BC\u03C0\u03BF\u03C1\u03B5\u03AF \u03BD\u03B1 \u03B8\u03B5\u03C9\u03C1\u03B7\u03B8\u03B5\u03AF \u03C9\u03C2 \u03AD\u03BD\u03B1 \u03C4\u03C1\u03BF\u03C0\u03BF\u03C0\u03BF\u03B9\u03B7\u03BC\u03AD\u03BD\u03BF \u03BA\u03B1\u03C1\u03C4\u03B5\u03C3\u03B9\u03B1\u03BD\u03CC \u03B5\u03C0\u03AF\u03C0\u03B5\u03B4\u03BF, \u03BC\u03B5 \u03C4\u03BF \u03C0\u03C1\u03B1\u03B3\u03BC\u03B1\u03C4\u03B9\u03BA\u03CC \u03BC\u03AD\u03C1\u03BF\u03C2 \u03C4\u03BF\u03C5 \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03BF\u03CD \u03B1\u03C1\u03B9\u03B8\u03BC\u03BF\u03CD \u03B1\u03BD\u03B1\u03C0\u03B1\u03C1\u03B9\u03C3\u03C4\u03CE\u03BD\u03C4\u03B1\u03C2 \u03BC\u03B5 \u03BC\u03B9\u03B1 \u03BC\u03B5\u03C4\u03B1\u03C4\u03CC\u03C0\u03B9\u03C3\u03B7 \u03BA\u03B1\u03C4\u03AC \u03BC\u03AE\u03BA\u03BF\u03C2 \u03C4\u03BF\u03C5 \u03AC\u03BE\u03BF\u03BD\u03B1 \u03C7, \u03BA\u03B1\u03B9 \u03C4\u03BF \u03C6\u03B1\u03BD\u03C4\u03B1\u03C3\u03C4\u03B9\u03BA\u03CC \u03BC\u03AD\u03C1\u03BF\u03C2 \u03BC\u03B5 \u03BC\u03AF\u03B1 \u03BC\u03B5\u03C4\u03B1\u03C4\u03CC\u03C0\u03B9\u03C3\u03B7 \u03BA\u03B1\u03C4\u03AC \u03BC\u03AE\u03BA\u03BF\u03C2 \u03C4\u03BF\u03C5 \u03AC\u03BE\u03BF\u03BD\u03B1 y."@el , "Bidang kompleks (terkadang disebut bidang Argan atau bidang Gauss) adalah sebuah bidang yang dibentuk oleh bilangan kompleks melalui sistem koordinat Kartesius. Sumbu- pada bidang tersebut merepresentasikan garis real yang disebut bagian real, sementara sumbu- merepresentasikan garis imajiner yang disebut bagian imajiner. Bidang kompleks dilambangkan ."@in , "En komplex vektor \u00E4r att med ett tv\u00E5dimensionellt koordinatsystem visualisera ett komplext tal i ett komplext linj\u00E4rt rum d\u00E4r x-axeln \u00E4r den reella delen och y-axeln \u00E4r den imagin\u00E4ra delen (arganddiagram). F\u00F6r det komplexa talet z \u00E4r vektorns l\u00E4ngd absolutbeloppet av z:"@sv , "En matem\u00E1ticas, el plano complejo es una forma de visualizar y ordenar el conjunto de los n\u00FAmeros complejos. Puede entenderse como un plano cartesiano modificado, en el que la parte real est\u00E1 representada en el eje de abscisas y la parte imaginaria en el eje de ordenadas. El eje de abscisas tambi\u00E9n recibe el nombre de eje real y el eje de ordenadas el nombre de eje imaginario. Asimismo, el conjunto de los n\u00FAmeros complejos se puede representar en su forma polar o trigonom\u00E9trica, formando as\u00ED un plano polar, en el que el valor absoluto, m\u00F3dulo o magnitud representa la longitud de un vector y su argumento es equivalente al \u00E1ngulo del mencionado vector, excepto el complejo 0 que no tiene argumento."@es , "Matematikan, plano konplexua edo z-planoa zenbaki konplexuak bi dimentsiotan irudikatzeko erabiltzen den irudikapen geometrikoa da. Planoak ardatz kartesiarren sistema bat du; abzisa ardatz erreala da eta ordenatua ardatz irudikaria, eta z = x + yi zenbaki konplexuari planoko (x,y) koordenatuak ematen zaizkio. Batzuetan, plano konplexuak Arganden planoa izena ere hartzen du Arganden diagramengatik. Plano konplexuaren sorrera egozten zaio, nahiz eta jatorrian Caspar Wessel norvegiar-daniar inkestatzaileak eta matematikariak deskribatua izan."@eu , "En math\u00E9matiques, le plan complexe (aussi appel\u00E9 plan d'Argand, plan d'Argand-Cauchy ou plan d'Argand-Gauss) d\u00E9signe un plan, muni d'un rep\u00E8re orthonorm\u00E9, dont chaque point est la repr\u00E9sentation graphique d'un nombre complexe unique. Le complexe associ\u00E9 \u00E0 un point est appel\u00E9 l'affixe de ce point. Une affixe est constitu\u00E9e d'une partie r\u00E9elle et d'une partie imaginaire correspondant respectivement \u00E0 l'abscisse et l'ordonn\u00E9e du point."@fr , "\uC218\uD559\uC5D0\uC11C, \uBCF5\uC18C\uD3C9\uBA74(\u8907\u7D20\u5E73\u9762)\uC740 \uBCF5\uC18C\uC218\uB97C \uAE30\uD558\uD559\uC801\uC73C\uB85C \uD45C\uD604\uD558\uAE30 \uC704\uD574 \uAC1C\uBC1C\uB41C \uC88C\uD45C\uD3C9\uBA74\uC73C\uB85C \uC11C\uB85C \uC9C1\uAD50\uD558\uB294 \uC2E4\uC218\uCD95\uACFC \uD5C8\uC218\uCD95\uC73C\uB85C \uC774\uB8E8\uC5B4\uC838 \uC788\uB2E4. \uC774\uAC83\uC740 \uBCF5\uC18C\uC218\uC758 \uC2E4\uC218\uBD80\uAC00 \uC2E4\uC218\uCD95\uC5D0, \uD5C8\uC218\uBD80\uAC00 \uD5C8\uC218\uCD95\uC5D0 \uB300\uC751\uB41C \uD615\uD0DC\uC758 \uB370\uCE74\uB974\uD2B8 \uC88C\uD45C\uB85C \uBCFC \uC218 \uC788\uB2E4. \uBCF5\uC18C\uD3C9\uBA74\uC758 \uAC1C\uB150\uC740 \uBCF5\uC18C\uC218\uC758 \uAE30\uD558\uD559\uC801 \uD574\uC11D\uC744 \uAC00\uB2A5\uD558\uAC8C \uD55C\uB2E4. \uB367\uC148\uC5F0\uC0B0 \uD558\uC5D0\uC11C, \uBCF5\uC18C\uC218\uB4E4\uC740 \uBCF5\uC18C\uD3C9\uBA74\uC0C1\uC5D0\uC11C \uBCA1\uD130\uCC98\uB7FC \uB354\uD574\uC9C4\uB2E4. \uB450 \uBCF5\uC18C\uC218\uC758 \uACF1\uC148\uC740 \uADF9\uC88C\uD45C\uB97C \uC774\uC6A9\uD558\uBA74 \uC27D\uAC8C \uD45C\uD604\uD560 \uC218 \uC788\uB2E4. \uD2B9\uD788 \uBCF5\uC18C\uC218\uC758 \uD06C\uAE30\uAC00 1\uC778 \uBCF5\uC18C\uC218 \uAC04\uC758 \uACF1\uC148\uC740 \uD68C\uC804\uD558\uB294 \uAC83\uCC98\uB7FC \uD589\uB3D9\uD55C\uB2E4. \uC0BC\uAC01\uD568\uC218\uC758 \uB367\uC148\uC815\uB9AC\uC5D0 \uC758\uD558\uC5EC, \uAC00 \uB418\uC5B4 \uD68C\uC804\uD55C \uACB0\uACFC\uC640 \uAC19\uAC8C \uB41C\uB2E4."@ko , "In analisi complessa, il piano complesso (chiamato anche piano di Argand-Gauss) \u00E8 una rappresentazione bidimensionale dell'insieme dei numeri complessi. Pu\u00F2 essere pensato come un piano cartesiano modificato, con la parte reale rappresentata sull'asse delle ascisse, detto per questo asse reale, e la parte immaginaria rappresentata sull'asse delle ordinate, detto quindi asse immaginario."@it , "En matematiko, la kompleksa ebeno estas vojo de videbligo de spaco de la kompleksaj nombroj. \u011Ci estas 2-dimensia e\u016Dklida ebeno kun karteziaj koordinatoj, kun la reela parto prezentata en la abscisa akso kaj la imaginara parto prezentata en la ordinata akso. La abscisa akso estas nomata anka\u016D kiel la reela akso kaj la ordinata akso estas nomata anka\u016D kiel la imaginara akso."@eo , "In de wiskunde is het complexe vlak een geometrische weergave van de complexe getallen, bestaande uit een re\u00EBle as en loodrecht daarop geplaatst de imaginaire as. Het complexe vlak kan worden gezien als een aangepast cartesische vlak, waar het re\u00EBle deel van een complex getal wordt weergegeven door een verplaatsing langs de x-as en het imaginaire deel door een verplaatsing langs de y-as."@nl , "\u0627\u0644\u0645\u0633\u062A\u0648\u0649 \u0627\u0644\u0639\u0642\u062F\u064A (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Complex plane)\u200F \u0647\u0648 \u062A\u0645\u062B\u064A\u0644 \u0647\u0646\u062F\u0633\u064A \u0644\u0644\u0623\u0639\u062F\u0627\u062F \u0627\u0644\u0645\u0631\u0643\u0628\u0629 \u0645\u0643\u0648\u0646 \u0645\u0646 \u0645\u062D\u0648\u0631 \u0627\u0644\u0623\u0639\u062F\u0627\u062F \u0627\u0644\u062D\u0642\u064A\u0642\u064A\u0629 \u0648\u0645\u062D\u0648\u0631 \u0627\u0644\u0623\u0639\u062F\u0627\u062F \u0627\u0644\u062A\u062E\u064A\u0644\u064A\u0629\u060C \u0627\u0644\u0639\u0645\u0648\u062F\u064A \u0639\u0644\u064A\u0647. \u0641\u064A \u0628\u0639\u0636 \u0627\u0644\u0623\u062D\u064A\u0627\u0646\u060C \u064A\u0637\u0644\u0642 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062A\u0648\u0649 \u0627\u0644\u0639\u0642\u062F\u064A \u0627\u0633\u0645 \u0645\u0633\u062A\u0648\u0649 \u0623\u0631\u063A\u0646\u062F \u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u062C\u0648\u0646 \u0631\u0648\u0628\u0631\u062A \u0623\u0631\u063A\u0646\u062F (1768-1822)."@ar , "O plano complexo, tamb\u00E9m chamado de Plano de Argand-Gauss ou Diagrama de Argand, \u00E9 um plano cartesiano usado para representar n\u00FAmeros complexos geometricamente. Nele, a parte imagin\u00E1ria de um n\u00FAmero complexo \u00E9 representada pela ordenada e a parte real pela abcissa. Desta forma um n\u00FAmero complexo z como 3 - 5i pode ser representado atrav\u00E9s do ponto (afixo ou imagem, quando z est\u00E1 na forma trigonom\u00E9trica) (3, -5) no plano de Argand-Gauss."@pt , "In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the x-axis, called the real axis, is formed by the real numbers, and the y-axis, called the imaginary axis, is formed by the imaginary numbers. The complex plane is sometimes known as the Argand plane or Gauss plane."@en , "\u041A\u043E\u0301\u043C\u043F\u043B\u0435\u0301\u043A\u0441\u043D\u0430\u044F \u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u044C \u2014 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u044B\u0445 \u0447\u0438\u0441\u0435\u043B . \u0422\u043E\u0447\u043A\u0430 \u0434\u0432\u0443\u043C\u0435\u0440\u043D\u043E\u0439 \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u043E\u0439 \u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u0438 , \u0438\u043C\u0435\u044E\u0449\u0430\u044F \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442\u044B , \u0438\u0437\u043E\u0431\u0440\u0430\u0436\u0430\u0435\u0442 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0435 \u0447\u0438\u0441\u043B\u043E , \u0433\u0434\u0435: \u2014 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u0430\u044F (\u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u0430\u044F) \u0447\u0430\u0441\u0442\u044C \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0433\u043E \u0447\u0438\u0441\u043B\u0430, \u2014 \u0435\u0433\u043E \u043C\u043D\u0438\u043C\u0430\u044F \u0447\u0430\u0441\u0442\u044C. \u0414\u0440\u0443\u0433\u0438\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438, \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u043C\u0443 \u0447\u0438\u0441\u043B\u0443 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0440\u0430\u0434\u0438\u0443\u0441-\u0432\u0435\u043A\u0442\u043E\u0440 \u0441 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442\u0430\u043C\u0438 \u0410\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u043C \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u044F\u043C \u043D\u0430\u0434 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u044B\u043C\u0438 \u0447\u0438\u0441\u043B\u0430\u043C\u0438 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044E\u0442 \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u0438 \u043D\u0430\u0434 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044E\u0449\u0438\u043C\u0438 \u0438\u043C \u0442\u043E\u0447\u043A\u0430\u043C\u0438 \u0438\u043B\u0438 \u0432\u0435\u043A\u0442\u043E\u0440\u0430\u043C\u0438. \u0422\u0435\u043C \u0441\u0430\u043C\u044B\u043C \u0440\u0430\u0437\u043B\u0438\u0447\u043D\u044B\u0435 \u0441\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u044F \u043C\u0435\u0436\u0434\u0443 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u044B\u043C\u0438 \u0447\u0438\u0441\u043B\u0430\u043C\u0438 \u043F\u043E\u043B\u0443\u0447\u0430\u044E\u0442 \u043D\u0430\u0433\u043B\u044F\u0434\u043D\u043E\u0435 \u0438\u0437\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u0438\u0435 \u043D\u0430 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0439 \u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u0438:"@ru ; rdfs:seeAlso dbr:Complex_number . @prefix foaf: . dbr:Complex_plane foaf:depiction , , . @prefix dct: . @prefix dbc: . dbr:Complex_plane dct:subject dbc:Classical_control_theory , dbc:Complex_numbers , dbc:Complex_analysis ; dbo:abstract "Matematikan, plano konplexua edo z-planoa zenbaki konplexuak bi dimentsiotan irudikatzeko erabiltzen den irudikapen geometrikoa da. Planoak ardatz kartesiarren sistema bat du; abzisa ardatz erreala da eta ordenatua ardatz irudikaria, eta z = x + yi zenbaki konplexuari planoko (x,y) koordenatuak ematen zaizkio. Batzuetan, plano konplexuak Arganden planoa izena ere hartzen du Arganden diagramengatik. Plano konplexuaren sorrera egozten zaio, nahiz eta jatorrian Caspar Wessel norvegiar-daniar inkestatzaileak eta matematikariak deskribatua izan."@eu , "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u8907\u7D20\u5E73\u9762\uFF08\u3075\u304F\u305D\u3078\u3044\u3081\u3093\u3001\u72EC: Komplexe Zahlenebene, \u82F1: complex plane\uFF09\u3042\u308B\u3044\u306F\u6570\u5E73\u9762\uFF08\u3059\u3046\u3078\u3044\u3081\u3093\u3001\u72EC: Zahlenebene\uFF09\u3001z-\u5E73\u9762\u3068\u306F\u3001\u8907\u7D20\u6570 z = x + iy \u3092\u76F4\u4EA4\u5EA7\u6A19 (x, y) \u306B\u5BFE\u5FDC\u3055\u305B\u305F\u76F4\u4EA4\u5EA7\u6A19\u5E73\u9762\u306E\u3053\u3068\u3067\u3042\u308B\u3002\u8907\u7D20\u6570\u306E\u5B9F\u90E8\u3092\u8868\u3059\u8EF8\u3092\u5B9F\u8EF8 (real axis)\uFF08\u5B9F\u6570\u76F4\u7DDA\uFF09\u3001\u865A\u90E8\u3092\u8868\u3059\u8EF8\u3092\u865A\u8EF8 (imaginary axis) \u3068\u3044\u3046\u3002 1811\u5E74\u9803\u306B\u30AC\u30A6\u30B9\u306B\u3088\u3063\u3066\u5C0E\u5165\u3055\u308C\u305F\u305F\u3081\u3001\u30AC\u30A6\u30B9\u5E73\u9762 (Gaussian plane) \u3068\u3082\u547C\u3070\u308C\u308B\u3002\u4E00\u65B9\u3001\u305D\u308C\u306B\u5148\u7ACB\u30641806\u5E74\u306B \u3082\u540C\u69D8\u306E\u624B\u6CD5\u3092\u7528\u3044\u305F\u305F\u3081\u3001\u30A2\u30EB\u30AC\u30F3\u56F3 (Argand Diagram) \u3068\u3082\u547C\u3070\u308C\u3066\u3044\u308B\u3002\u3055\u3089\u306B\u3001\u305D\u308C\u4EE5\u524D\u306E1797\u5E74\u306E \u306E\u66F8\u7C21\u306B\u3082\u767B\u5834\u3057\u3066\u3044\u308B\u3002\u3053\u306E\u3088\u3046\u306B\u8907\u7D20\u6570\u306E\u5E7E\u4F55\u7684\u8868\u793A\u306F\u30AC\u30A6\u30B9\u4EE5\u524D\u306B\u3082\u77E5\u3089\u308C\u3066\u3044\u305F\u304C\u3001\u4ECA\u65E5\u7528\u3044\u3089\u308C\u3066\u3044\u308B\u3088\u3046\u306A\u5F62\u5F0F\u3067\u8907\u7D20\u5E73\u9762\u3092\u8AD6\u3058\u305F\u306E\u306F\u30AC\u30A6\u30B9\u3067\u3042\u308B\u3002\u4E09\u8005\u306E\u540D\u524D\u3092\u3068\u3063\u3066\u30AC\u30A6\u30B9\u30FB\u30A2\u30EB\u30AC\u30F3\u5E73\u9762\u3001\u30AC\u30A6\u30B9\u30FB\u30A6\u30A7\u30C3\u30BB\u30EB\u5E73\u9762\u306A\u3069\u3068\u3082\u8A00\u308F\u308C\u308B\u3002 \u82F1\u79F0 complex plane \u306E\u8A33\u3068\u3057\u3066\u8907\u7D20\u6570\u5E73\u9762\u3068\u547C\u3076\u3053\u3068\u3082\u5C11\u306A\u304F\u306A\u304F\u3001\u5927\u5B66\u4EE5\u4E0A\u306E\u6570\u5B66\u66F8\u3067\u306F\u300E\u8907\u7D20\u5E73\u9762\u300F\u307E\u305F\u306F\u300E\u30AC\u30A6\u30B9\u5E73\u9762\u300F\u306E\u65B9\u304C\u3014\u8907\u7D20\u6570\u5E73\u9762\u3088\u308A\u3082\u3015\u5727\u5012\u7684\u306B\u4E3B\u6D41\u3067\u3042\u308B\u3068\u306E\u898B\u89E3\u304C\u3042\u308B\u3002\u3057\u304B\u3057\u3001\u63A5\u982D\u8F9E\u300C\u8907\u7D20\u2014\u300D\u3092\u300C\u4FC2\u6570\u4F53\u3092\u8907\u7D20\u6570\u4F53\u3068\u3059\u308B\u300D\u3068\u3044\u3046\u610F\u5473\u306B\u89E3\u91C8\u3059\u308B\u3068\u3001\u8907\u7D20\u6570\u3092\u6210\u5206\u3068\u3059\u308B\u300C\u5E73\u9762\u300D\u3068\u3044\u3046\u610F\u5473\u306B\u306A\u308A\u3001C2\uFF08\u5B9F\u90E8\u3068\u865A\u90E8\u306B\u5206\u3051\u308B\u3068\u5B9F4\u6B21\u5143\u7DDA\u5F62\u7A7A\u9593\uFF09\uFF08\u4E8C\u6B21\u5143\u8907\u7D20\u89E3\u6790\u7A7A\u9593\uFF09\u3092\u6307\u3059\u306E\u3067\u3001\u6587\u8108\u306B\u3088\u3063\u3066\u3069\u3061\u3089\u3092\u6307\u3057\u3066\u3044\u308B\u304B\u306F\u6CE8\u610F\u304C\u5FC5\u8981\u3067\u3042\u308B\u3002\u65E5\u672C\u306E\u9AD8\u7B49\u5B66\u6821\u306E\u5B66\u7FD2\u6307\u5C0E\u8981\u9818\u3067\u306F\u73FE\u5728\u306F\u300C\u8907\u7D20\u6570\u5E73\u9762\u300D\u304C\u7528\u3044\u3089\u308C\u3066\u3044\u308B\u3002"@ja , "\u041A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0430 \u043F\u043B\u043E\u0449\u0438\u043D\u0430 \u2014 \u043C\u043D\u043E\u0436\u0438\u043D\u0430 \u0432\u043F\u043E\u0440\u044F\u0434\u043A\u043E\u0432\u0430\u043D\u0438\u0445 \u043F\u0430\u0440 , \u0434\u0435 . \u0417\u0430\u0437\u0432\u0438\u0447\u0430\u0439 \u043F\u0440\u043E\u0432\u043E\u0434\u0438\u0442\u044C\u0441\u044F \u0443\u0442\u043E\u0442\u043E\u0436\u043D\u0435\u043D\u043D\u044F \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0457 \u043F\u043B\u043E\u0449\u0438\u043D\u0438 \u0456 \u043F\u043E\u043B\u044F \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0438\u0445 \u0447\u0438\u0441\u0435\u043B \u0437\u0430 \u043F\u0440\u0438\u043D\u0446\u0438\u043F\u043E\u043C . \u0426\u0435 \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u0454 \u0432\u0432\u0435\u0441\u0442\u0438 \u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0456 \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u0457 \u043D\u0430 \u043F\u043B\u043E\u0449\u0438\u043D\u0456 . \u0420\u043E\u0437\u0433\u043B\u044F\u043D\u0435\u043C\u043E \u0442\u043E\u043F\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u0456 \u0432\u043B\u0430\u0441\u0442\u0438\u0432\u043E\u0441\u0442\u0456 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0457 \u043F\u043B\u043E\u0449\u0438\u043D\u0438 \u0456 \u043D\u0435 \u0431\u0443\u0434\u0435\u043C\u043E \u043F\u0440\u043E\u0432\u043E\u0434\u0438\u0442\u0438 \u0440\u0456\u0437\u043D\u0438\u0446\u0456 \u043C\u0456\u0436 \u043F\u0430\u0440\u043E\u044E \u0456 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0438\u043C \u0447\u0438\u0441\u043B\u043E\u043C . \u041A\u043E\u043D\u0446\u0435\u043F\u0446\u0456\u044F \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0457 \u043F\u043B\u043E\u0449\u0438\u043D\u0438, \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u0454 \u043F\u0440\u0438\u0432\u0435\u0441\u0442\u0438 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0456 \u0447\u0438\u0441\u043B\u0430 \u0443 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u043E\u043C\u0443 \u0441\u0435\u043D\u0441\u0456. \u041E\u043F\u0435\u0440\u0430\u0446\u0456\u044E \u0434\u043E\u0434\u0430\u0432\u0430\u043D\u043D\u044F, \u0437\u0434\u0456\u0439\u0441\u043D\u044E\u0432\u0430\u0442\u0438 \u044F\u043A \u0434\u043E\u0434\u0430\u0432\u0430\u043D\u043D\u044F \u0432\u0435\u043A\u0442\u043E\u0440\u0456\u0432. \u041C\u043D\u043E\u0436\u0435\u043D\u043D\u044F \u0434\u0432\u043E\u0445 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0438\u0445 \u0447\u0438\u0441\u0435\u043B \u043C\u043E\u0436\u043D\u0430 \u0443 \u043D\u0430\u0439\u043F\u0440\u043E\u0441\u0442\u0456\u0448\u043E\u043C\u0443 \u0432\u0438\u0433\u043B\u044F\u0434\u0456 \u043C\u043E\u0436\u043D\u0430 \u0432\u0438\u0440\u0430\u0437\u0438\u0442\u0438 \u0432 \u043F\u043E\u043B\u044F\u0440\u043D\u0438\u0445 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442\u0430\u0445\u2014\u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0430 \u0430\u0431\u043E \u043C\u043E\u0434\u0443\u043B\u044C \u0434\u043E\u0431\u0443\u0442\u043A\u0443 \u0446\u0435 \u0434\u043E\u0431\u0443\u0442\u043E\u043A \u0434\u0432\u043E\u0445 \u0430\u0431\u0441\u043E\u043B\u044E\u0442\u043D\u0438\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D, \u0430\u0431\u043E \u043C\u043E\u0434\u0443\u043B\u0456\u0432, \u0430 \u043A\u0443\u0442 \u0430\u0431\u043E \u0430\u0440\u0433\u0443\u043C\u0435\u043D\u0442 \u0434\u043E\u0431\u0443\u0442\u043A\u0443 \u0454 \u0441\u0443\u043C\u043E\u044E \u0434\u0432\u043E\u0445 \u043A\u0443\u0442\u0456\u0432, \u0430\u0431\u043E \u0430\u0440\u0433\u0443\u043C\u0435\u043D\u0442\u0456\u0432. \u0417\u043E\u043A\u0440\u0435\u043C\u0430, \u043C\u043D\u043E\u0436\u0435\u043D\u043D\u044F \u043D\u0430 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0435 \u0447\u0438\u0441\u043B\u043E \u0456\u0437 \u043C\u043E\u0434\u0443\u043B\u0435\u043C, \u0449\u043E \u0434\u043E\u0440\u0456\u0432\u043D\u044E\u0454 1 \u043F\u0440\u0438\u0432\u043E\u0434\u0438\u0442\u044C \u0434\u043E \u043E\u0431\u0435\u0440\u0442\u0430\u043D\u043D\u044F. \u041A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0443 \u043F\u043B\u043E\u0449\u0438\u043D\u0443 \u0456\u043D\u043E\u0434\u0456 \u043D\u0430\u0437\u0438\u0432\u0430\u044E\u0442\u044C \u043F\u043B\u043E\u0449\u0438\u043D\u043E\u044E \u0410\u0440\u0433\u0430\u043D\u0434\u0430, \u0430 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0456 \u043D\u0430 \u0446\u0456\u0439 \u043F\u043B\u043E\u0449\u0438\u043D\u0456 \u0434\u0456\u0430\u0433\u0440\u0430\u043C\u0430\u043C\u0438 \u0410\u0440\u0433\u0430\u043D\u0434\u0430. \u0412\u043E\u043D\u0438 \u043D\u0435\u0437\u0432\u0430\u043D\u0456 \u0432 \u0447\u0435\u0441\u0442\u044C (1768\u20141822), \u0445\u043E\u0447\u0430 \u0432\u043F\u0435\u0440\u0448\u0435 \u0457\u0445 \u043E\u043F\u0438\u0441\u0430\u0432 \u043D\u043E\u0440\u0432\u0435\u0437\u044C\u043A\u043E-\u0434\u0430\u0442\u0441\u044C\u043A\u0438\u0439 \u0437\u0435\u043C\u043B\u0435\u0432\u043F\u043E\u0440\u044F\u0434\u043D\u0438\u043A \u0456 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A (1745\u20141818)."@uk , "En matematiko, la kompleksa ebeno estas vojo de videbligo de spaco de la kompleksaj nombroj. \u011Ci estas 2-dimensia e\u016Dklida ebeno kun karteziaj koordinatoj, kun la reela parto prezentata en la abscisa akso kaj la imaginara parto prezentata en la ordinata akso. La abscisa akso estas nomata anka\u016D kiel la reela akso kaj la ordinata akso estas nomata anka\u016D kiel la imaginara akso. La koncepto de la kompleksa ebeno permesas geometrian interpretadon de kompleksaj nombroj. Por adicio, oni adicias same kiel vektoroj, kaj la multipliko de kompleksaj nombroj povas esti esprimita simple per uzo de polusaj koordinatoj, kie la grandeco de la produto estas la produto de tiuj de la faktoroj, kaj la angulo de la reela akso de la produto estas la sumo de tiuj de la faktoroj."@eo , "Bidang kompleks (terkadang disebut bidang Argan atau bidang Gauss) adalah sebuah bidang yang dibentuk oleh bilangan kompleks melalui sistem koordinat Kartesius. Sumbu- pada bidang tersebut merepresentasikan garis real yang disebut bagian real, sementara sumbu- merepresentasikan garis imajiner yang disebut bagian imajiner. Bidang kompleks dilambangkan ."@in , "En matem\u00E1ticas, el plano complejo es una forma de visualizar y ordenar el conjunto de los n\u00FAmeros complejos. Puede entenderse como un plano cartesiano modificado, en el que la parte real est\u00E1 representada en el eje de abscisas y la parte imaginaria en el eje de ordenadas. El eje de abscisas tambi\u00E9n recibe el nombre de eje real y el eje de ordenadas el nombre de eje imaginario. Asimismo, el conjunto de los n\u00FAmeros complejos se puede representar en su forma polar o trigonom\u00E9trica, formando as\u00ED un plano polar, en el que el valor absoluto, m\u00F3dulo o magnitud representa la longitud de un vector y su argumento es equivalente al \u00E1ngulo del mencionado vector, excepto el complejo 0 que no tiene argumento."@es , "En math\u00E9matiques, le plan complexe (aussi appel\u00E9 plan d'Argand, plan d'Argand-Cauchy ou plan d'Argand-Gauss) d\u00E9signe un plan, muni d'un rep\u00E8re orthonorm\u00E9, dont chaque point est la repr\u00E9sentation graphique d'un nombre complexe unique. Le complexe associ\u00E9 \u00E0 un point est appel\u00E9 l'affixe de ce point. Une affixe est constitu\u00E9e d'une partie r\u00E9elle et d'une partie imaginaire correspondant respectivement \u00E0 l'abscisse et l'ordonn\u00E9e du point."@fr , "En matem\u00E0tiques, el pla complex \u00E9s una forma de visualitzar l'espai dels nombres complexos. Pot entendre's com un pla cartesi\u00E0 modificat, en el que la part real est\u00E0 representada a l'eix x i la part imagin\u00E0ria a l'eix y. L'eix x tamb\u00E9 rep el nom d'eix real i l'eix y el d'eix imaginari. El pla complex tamb\u00E9 s'anomena Pla d'Argand, ja que s'utilitza en els diagrames d'Argand. Aquests porten el nom de Jean-Robert Argand (1768-1822). Els diagrames d'Argand s'usen sovint per representar les posicions dels pols i zeros d'una funci\u00F3 en el pla complex. El concepte de pla complex permet una dels nombres complexos. La suma de nombres complexos es pot relacionar amb la suma de vectors, i la multiplicaci\u00F3 de dos nombres complexos es pot expressar m\u00E9s f\u00E0cilment en coordenades polars - la magnitud o m\u00F2dul del producte \u00E9s el producte dels dos valors absoluts, o m\u00F2duls, i l'angle o argument del producte \u00E9s la suma dels dos angles, o arguments. En particular, la multiplicaci\u00F3 per un nombre complex de m\u00F2dul 1 actua com una rotaci\u00F3. La teoria de les funcions complexes \u00E9s una de les \u00E0rees m\u00E9s riques de la matem\u00E0tica, que troba aplicaci\u00F3 en moltes altres \u00E0rees de la matem\u00E0tica i tamb\u00E9 en f\u00EDsica, electr\u00F2nica i molts altres camps."@ca , "\u0627\u0644\u0645\u0633\u062A\u0648\u0649 \u0627\u0644\u0639\u0642\u062F\u064A (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Complex plane)\u200F \u0647\u0648 \u062A\u0645\u062B\u064A\u0644 \u0647\u0646\u062F\u0633\u064A \u0644\u0644\u0623\u0639\u062F\u0627\u062F \u0627\u0644\u0645\u0631\u0643\u0628\u0629 \u0645\u0643\u0648\u0646 \u0645\u0646 \u0645\u062D\u0648\u0631 \u0627\u0644\u0623\u0639\u062F\u0627\u062F \u0627\u0644\u062D\u0642\u064A\u0642\u064A\u0629 \u0648\u0645\u062D\u0648\u0631 \u0627\u0644\u0623\u0639\u062F\u0627\u062F \u0627\u0644\u062A\u062E\u064A\u0644\u064A\u0629\u060C \u0627\u0644\u0639\u0645\u0648\u062F\u064A \u0639\u0644\u064A\u0647. \u0641\u064A \u0628\u0639\u0636 \u0627\u0644\u0623\u062D\u064A\u0627\u0646\u060C \u064A\u0637\u0644\u0642 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062A\u0648\u0649 \u0627\u0644\u0639\u0642\u062F\u064A \u0627\u0633\u0645 \u0645\u0633\u062A\u0648\u0649 \u0623\u0631\u063A\u0646\u062F \u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u062C\u0648\u0646 \u0631\u0648\u0628\u0631\u062A \u0623\u0631\u063A\u0646\u062F (1768-1822)."@ar , "In analisi complessa, il piano complesso (chiamato anche piano di Argand-Gauss) \u00E8 una rappresentazione bidimensionale dell'insieme dei numeri complessi. Pu\u00F2 essere pensato come un piano cartesiano modificato, con la parte reale rappresentata sull'asse delle ascisse, detto per questo asse reale, e la parte immaginaria rappresentata sull'asse delle ordinate, detto quindi asse immaginario."@it , "En komplex vektor \u00E4r att med ett tv\u00E5dimensionellt koordinatsystem visualisera ett komplext tal i ett komplext linj\u00E4rt rum d\u00E4r x-axeln \u00E4r den reella delen och y-axeln \u00E4r den imagin\u00E4ra delen (arganddiagram). F\u00F6r det komplexa talet z \u00E4r vektorns l\u00E4ngd absolutbeloppet av z:"@sv , "P\u0142aszczyzna zespolona, p\u0142aszczyzna Gaussa \u2013 geometryczny model cia\u0142a liczb zespolonych P\u0142aszczyzna pe\u0142ni w nim w stosunku do liczb zespolonych rol\u0119 analogiczn\u0105 do roli, kt\u00F3r\u0105 pe\u0142ni wzgl\u0119dem cia\u0142a liczb rzeczywistych. Na p\u0142aszczy\u017Anie wprowadzamy najpierw prostok\u0105tny kartezja\u0144ski uk\u0142ad wsp\u00F3\u0142rz\u0119dnych, na kt\u00F3ry sk\u0142adaj\u0105 si\u0119 dwie prostopad\u0142e do siebie osie wsp\u00F3\u0142rz\u0119dnych przecinaj\u0105ce si\u0119 we wsp\u00F3lnym pocz\u0105tku Jedna z osi, o\u015B jest pozioma (o\u015B odci\u0119tych), skierowana od lewej strony do prawej, a druga pionowa (o\u015B rz\u0119dnych), jest skierowana od do\u0142u do g\u00F3ry. Ka\u017Cdy punkt p\u0142aszczyzny jest jednoznacznie opisywany przez dwie wsp\u00F3\u0142rz\u0119dne: odci\u0119t\u0105 i rz\u0119dn\u0105 b\u0119d\u0105ce odpowiednio wsp\u00F3\u0142rz\u0119dnymi rzut\u00F3w punktu na o\u015B odci\u0119tych i o\u015B rz\u0119dnych. Ka\u017Cdemu tak opisanemu punktowi p\u0142aszczyzny mo\u017Cna przyporz\u0105dkowa\u0107 liczb\u0119 zespolon\u0105 : gdzie Przyporz\u0105dkowanie to jest r\u00F3\u017Cnowarto\u015Bciowe i obrazem p\u0142aszczyzny jest w nim zbi\u00F3r wszystkich liczb zespolonych. Zatem oba zbiory mo\u017Cna uto\u017Csami\u0107. W zwi\u0105zku z tym o\u015B odci\u0119tych nazywa si\u0119 osi\u0105 rzeczywist\u0105, a o\u015B rz\u0119dnych \u2013 osi\u0105 urojon\u0105 (od pierwiastka kwadratowego z minus jedynki, nazywanego pierwiastkiem urojonym). Zapisujemy to nast\u0119puj\u0105co: Dzia\u0142ania na liczbach zespolonych okre\u015Bla si\u0119 nast\u0119puj\u0105co. Niech Wtedy St\u0105d wynika, \u017Ce dzia\u0142ania dodawania i mno\u017Cenia na p\u0142aszczy\u017Anie mo\u017Cna okre\u015Bli\u0107 nast\u0119puj\u0105co: Z definicji tych wynika, \u017Ce: \n* Dla punkt\u00F3w le\u017C\u0105cych na osi rzeczywistej oba dzia\u0142ania mo\u017Cna uto\u017Csami\u0107 z dzia\u0142aniami na liczbach rzeczywistych. \n* Dla dowolnego punktu prawdziwa jest r\u00F3wno\u015B\u0107 \n* i bardziej og\u00F3lnie co oznacza, \u017Ce mno\u017Cenie przez mo\u017Cna zinterpretowa\u0107 na p\u0142aszczy\u017Anie jako obr\u00F3t doko\u0142a \u015Brodka wsp\u00F3\u0142rz\u0119dnych o k\u0105t 90\u00B0."@pl , "\uC218\uD559\uC5D0\uC11C, \uBCF5\uC18C\uD3C9\uBA74(\u8907\u7D20\u5E73\u9762)\uC740 \uBCF5\uC18C\uC218\uB97C \uAE30\uD558\uD559\uC801\uC73C\uB85C \uD45C\uD604\uD558\uAE30 \uC704\uD574 \uAC1C\uBC1C\uB41C \uC88C\uD45C\uD3C9\uBA74\uC73C\uB85C \uC11C\uB85C \uC9C1\uAD50\uD558\uB294 \uC2E4\uC218\uCD95\uACFC \uD5C8\uC218\uCD95\uC73C\uB85C \uC774\uB8E8\uC5B4\uC838 \uC788\uB2E4. \uC774\uAC83\uC740 \uBCF5\uC18C\uC218\uC758 \uC2E4\uC218\uBD80\uAC00 \uC2E4\uC218\uCD95\uC5D0, \uD5C8\uC218\uBD80\uAC00 \uD5C8\uC218\uCD95\uC5D0 \uB300\uC751\uB41C \uD615\uD0DC\uC758 \uB370\uCE74\uB974\uD2B8 \uC88C\uD45C\uB85C \uBCFC \uC218 \uC788\uB2E4. \uBCF5\uC18C\uD3C9\uBA74\uC758 \uAC1C\uB150\uC740 \uBCF5\uC18C\uC218\uC758 \uAE30\uD558\uD559\uC801 \uD574\uC11D\uC744 \uAC00\uB2A5\uD558\uAC8C \uD55C\uB2E4. \uB367\uC148\uC5F0\uC0B0 \uD558\uC5D0\uC11C, \uBCF5\uC18C\uC218\uB4E4\uC740 \uBCF5\uC18C\uD3C9\uBA74\uC0C1\uC5D0\uC11C \uBCA1\uD130\uCC98\uB7FC \uB354\uD574\uC9C4\uB2E4. \uB450 \uBCF5\uC18C\uC218\uC758 \uACF1\uC148\uC740 \uADF9\uC88C\uD45C\uB97C \uC774\uC6A9\uD558\uBA74 \uC27D\uAC8C \uD45C\uD604\uD560 \uC218 \uC788\uB2E4. \uD2B9\uD788 \uBCF5\uC18C\uC218\uC758 \uD06C\uAE30\uAC00 1\uC778 \uBCF5\uC18C\uC218 \uAC04\uC758 \uACF1\uC148\uC740 \uD68C\uC804\uD558\uB294 \uAC83\uCC98\uB7FC \uD589\uB3D9\uD55C\uB2E4. \uC0BC\uAC01\uD568\uC218\uC758 \uB367\uC148\uC815\uB9AC\uC5D0 \uC758\uD558\uC5EC, \uAC00 \uB418\uC5B4 \uD68C\uC804\uD55C \uACB0\uACFC\uC640 \uAC19\uAC8C \uB41C\uB2E4."@ko , "\u041A\u043E\u0301\u043C\u043F\u043B\u0435\u0301\u043A\u0441\u043D\u0430\u044F \u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u044C \u2014 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u044B\u0445 \u0447\u0438\u0441\u0435\u043B . \u0422\u043E\u0447\u043A\u0430 \u0434\u0432\u0443\u043C\u0435\u0440\u043D\u043E\u0439 \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u043E\u0439 \u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u0438 , \u0438\u043C\u0435\u044E\u0449\u0430\u044F \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442\u044B , \u0438\u0437\u043E\u0431\u0440\u0430\u0436\u0430\u0435\u0442 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0435 \u0447\u0438\u0441\u043B\u043E , \u0433\u0434\u0435: \u2014 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u0430\u044F (\u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u0430\u044F) \u0447\u0430\u0441\u0442\u044C \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0433\u043E \u0447\u0438\u0441\u043B\u0430, \u2014 \u0435\u0433\u043E \u043C\u043D\u0438\u043C\u0430\u044F \u0447\u0430\u0441\u0442\u044C. \u0414\u0440\u0443\u0433\u0438\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438, \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u043C\u0443 \u0447\u0438\u0441\u043B\u0443 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0440\u0430\u0434\u0438\u0443\u0441-\u0432\u0435\u043A\u0442\u043E\u0440 \u0441 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442\u0430\u043C\u0438 \u0410\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u043C \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u044F\u043C \u043D\u0430\u0434 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u044B\u043C\u0438 \u0447\u0438\u0441\u043B\u0430\u043C\u0438 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044E\u0442 \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u0438 \u043D\u0430\u0434 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044E\u0449\u0438\u043C\u0438 \u0438\u043C \u0442\u043E\u0447\u043A\u0430\u043C\u0438 \u0438\u043B\u0438 \u0432\u0435\u043A\u0442\u043E\u0440\u0430\u043C\u0438. \u0422\u0435\u043C \u0441\u0430\u043C\u044B\u043C \u0440\u0430\u0437\u043B\u0438\u0447\u043D\u044B\u0435 \u0441\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u044F \u043C\u0435\u0436\u0434\u0443 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u044B\u043C\u0438 \u0447\u0438\u0441\u043B\u0430\u043C\u0438 \u043F\u043E\u043B\u0443\u0447\u0430\u044E\u0442 \u043D\u0430\u0433\u043B\u044F\u0434\u043D\u043E\u0435 \u0438\u0437\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u0438\u0435 \u043D\u0430 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0439 \u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u0438: \n* \u0441\u043B\u043E\u0436\u0435\u043D\u0438\u044E \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u044B\u0445 \u0447\u0438\u0441\u0435\u043B \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0441\u043B\u043E\u0436\u0435\u043D\u0438\u0435 \u0440\u0430\u0434\u0438\u0443\u0441-\u0432\u0435\u043A\u0442\u043E\u0440\u043E\u0432; \n* \u0443\u043C\u043D\u043E\u0436\u0435\u043D\u0438\u044E \u043D\u0430 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0435 \u0447\u0438\u0441\u043B\u043E \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043F\u043E\u0432\u043E\u0440\u043E\u0442 \u0440\u0430\u0434\u0438\u0443\u0441-\u0432\u0435\u043A\u0442\u043E\u0440\u0430 \u043D\u0430 \u0443\u0433\u043E\u043B \u0438 \u0440\u0430\u0441\u0442\u044F\u0436\u0435\u043D\u0438\u0435 \u0440\u0430\u0434\u0438\u0443\u0441-\u0432\u0435\u043A\u0442\u043E\u0440\u0430 \u0432 \u0440\u0430\u0437; \n* \u043A\u043E\u0440\u043D\u0438 n-\u0439 \u0441\u0442\u0435\u043F\u0435\u043D\u0438 \u0438\u0437 \u0447\u0438\u0441\u043B\u0430 \u0440\u0430\u0441\u043F\u043E\u043B\u0430\u0433\u0430\u044E\u0442\u0441\u044F \u0432 \u0432\u0435\u0440\u0448\u0438\u043D\u0430\u0445 \u043F\u0440\u0430\u0432\u0438\u043B\u044C\u043D\u043E\u0433\u043E n-\u0443\u0433\u043E\u043B\u044C\u043D\u0438\u043A\u0430 \u0441 \u0446\u0435\u043D\u0442\u0440\u043E\u043C \u0432 \u043D\u0430\u0447\u0430\u043B\u0435 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442. \u041A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0437\u043D\u0430\u0447\u043D\u044B\u0435 \u0444\u0443\u043D\u043A\u0446\u0438\u0438 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0433\u043E \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u043E\u0433\u043E \u0438\u043D\u0442\u0435\u0440\u043F\u0440\u0435\u0442\u0438\u0440\u0443\u044E\u0442\u0441\u044F \u043A\u0430\u043A \u043E\u0442\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u0438\u044F \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u0439 \u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u0438 \u0432 \u0441\u0435\u0431\u044F. \u041E\u0441\u043E\u0431\u0443\u044E \u0440\u043E\u043B\u044C \u0432 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u043E\u043C \u0430\u043D\u0430\u043B\u0438\u0437\u0435 \u0438\u0433\u0440\u0430\u044E\u0442 \u043A\u043E\u043D\u0444\u043E\u0440\u043C\u043D\u044B\u0435 \u043E\u0442\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u0438\u044F."@ru , "In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the x-axis, called the real axis, is formed by the real numbers, and the y-axis, called the imaginary axis, is formed by the imaginary numbers. The complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors. The multiplication of two complex numbers can be expressed more easily in polar coordinates\u2014the magnitude or modulus of the product is the product of the two absolute values, or moduli, and the angle or argument of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as a rotation. The complex plane is sometimes known as the Argand plane or Gauss plane."@en , "O plano complexo, tamb\u00E9m chamado de Plano de Argand-Gauss ou Diagrama de Argand, \u00E9 um plano cartesiano usado para representar n\u00FAmeros complexos geometricamente. Nele, a parte imagin\u00E1ria de um n\u00FAmero complexo \u00E9 representada pela ordenada e a parte real pela abcissa. Desta forma um n\u00FAmero complexo z como 3 - 5i pode ser representado atrav\u00E9s do ponto (afixo ou imagem, quando z est\u00E1 na forma trigonom\u00E9trica) (3, -5) no plano de Argand-Gauss."@pt , "Komplexn\u00ED rovina (\u010Dasto t\u00E9\u017E Gaussova rovina) je v matematice zp\u016Fsob zobrazen\u00ED komplexn\u00EDch \u010D\u00EDsel. Ve frankofonn\u00ED literatu\u0159e b\u00FDv\u00E1 n\u011Bkdy ozna\u010Dov\u00E1na jako Argandova rovina, Cauchyho rovina nebo Argand\u016Fv diagram. Na osu x se vyn\u00E1\u0161\u00ED re\u00E1ln\u00E1 \u010D\u00E1st komplexn\u00EDho \u010D\u00EDsla z, tzn. , a proto je tato osa ozna\u010Dov\u00E1na jako re\u00E1ln\u00E1. Na osu y se vyn\u00E1\u0161\u00ED imagin\u00E1rn\u00ED \u010D\u00E1st komplexn\u00EDho \u010D\u00EDsla z, tzn. , a proto je tato osa ozna\u010Dov\u00E1na jako imagin\u00E1rn\u00ED. Komplexn\u00ED rovinu, do n\u00ED\u017E zahrnujeme i nevlastn\u00ED bod , ozna\u010Dujeme jako roz\u0161\u00ED\u0159enou rovinu (komplexn\u00EDch \u010D\u00EDsel). Tato z\u00FApln\u011Bn\u00E1 komplexn\u00ED \u010D\u00EDsla v\u0161ak n\u00E1zorn\u011Bji zobrazuje Riemannova koule. Na obr\u00E1zku je zobrazen vztah mezi komplexn\u00EDm \u010D\u00EDslem a \u010D\u00EDslem sdru\u017Een\u00FDm v komplexn\u00ED rovin\u011B. Zn\u00E1zor\u0148ujeme-li \u010D\u00EDsla t\u00EDmto zp\u016Fsobem, pak sou\u010Det dvou \u010D\u00EDsel odpov\u00EDd\u00E1 vektorov\u00E9mu sou\u010Dtu jejich pr\u016Fvodi\u010D\u016F (tzv. rovnob\u011B\u017En\u00EDkov\u00E9 pravidlo). P\u0159i n\u00E1soben\u00ED je argument sou\u010Dinu roven sou\u010Dtu argument\u016F jednotliv\u00FDch \u010Dinitel\u016F a absolutn\u00ED hodnota v\u00FDsledku je rovna sou\u010Dinu absolutn\u00EDch hodnot n\u00E1soben\u00FDch \u010D\u00EDsel. To geometricky odpov\u00EDd\u00E1 p\u0159\u00EDm\u00E9 podobnosti \u2014 oto\u010Den\u00ED okolo po\u010D\u00E1tku slo\u017Een\u00E9mu se stejnolehlost\u00ED se st\u0159edem v po\u010D\u00E1tku."@cs , "\u6570\u5B66\u4E2D\uFF0C\u590D\u5E73\u9762\uFF08\u82F1\u8A9E\uFF1AComplex plane\uFF09\u662F\u7528\u6C34\u5E73\u7684\u5B9E\u8F74\u4E0E\u5782\u76F4\u7684\u865A\u8F74\u5EFA\u7ACB\u8D77\u6765\u7684\u8907\u6578\u7684\u51E0\u4F55\u8868\u793A\u3002\u5B83\u53EF\u89C6\u4E3A\u4E00\u4E2A\u5177\u6709\u7279\u5B9A\u4EE3\u6570\u7ED3\u6784\u7B1B\u5361\u513F\u5E73\u9762\uFF08\u5B9E\u5E73\u9762\uFF09\uFF0C\u4E00\u4E2A\u590D\u6570\u7684\u5B9E\u90E8\u7528\u6CBF\u7740 x-\u8F74\u7684\u4F4D\u79FB\u8868\u793A\uFF0C\u865A\u90E8\u7528\u6CBF\u7740 y-\u8F74\u7684\u4F4D\u79FB\u8868\u793A\u3002 \u590D\u5E73\u9762\u6709\u65F6\u4E5F\u53EB\u505A\u963F\u5C14\u5188\u5E73\u9762\uFF0C\u56E0\u4E3A\u5B83\u7528\u4E8E\u963F\u5C14\u5188\u56FE\u4E2D\u3002\u8FD9\u662F\u4EE5\u8BA9-\u7F57\u8D1D\u5C14\u00B7\u963F\u5C14\u5188\uFF081768-1822\uFF09\u547D\u540D\u7684\uFF0C\u5C3D\u7BA1\u5B83\u4EEC\u6700\u5148\u662F\u632A\u5A01-\u4E39\u9EA6\u571F\u5730\u6D4B\u91CF\u5458\u548C\u6570\u5B66\u5BB6\u5361\u65AF\u5E15\u5C14\u00B7\u97E6\u585E\u5C14\uFF081745-1818\uFF09\u53D9\u8FF0\u7684\u3002\u963F\u5C14\u5188\u56FE\u7ECF\u5E38\u7528\u6765\u6807\u793A\u590D\u5E73\u9762\u4E0A\u51FD\u6570\u7684\u6781\u70B9\u4E0E\u96F6\u70B9\u7684\u4F4D\u7F6E\u3002 \u590D\u5E73\u9762\u7684\u60F3\u6CD5\u63D0\u4F9B\u4E86\u4E00\u4E2A\u590D\u6570\u7684\u51E0\u4F55\u89E3\u91CA\u3002\u5728\u52A0\u6CD5\u4E0B\uFF0C\u5B83\u4EEC\u50CF\u5411\u91CF\u4E00\u6837\u76F8\u52A0\uFF1B\u4E24\u4E2A\u590D\u6570\u7684\u4E58\u6CD5\u5728\u6781\u5750\u6807\u4E0B\u7684\u8868\u793A\u6700\u7B80\u5355\u2014\u2014\u4E58\u79EF\u7684\u957F\u5EA6\u6216\u6A21\u957F\u662F\u4E24\u4E2A\u7EDD\u5BF9\u503C\u6216\u6A21\u957F\u7684\u4E58\u79EF\uFF0C\u4E58\u79EF\u7684\u89D2\u5EA6\u6216\u8F90\u89D2\u662F\u4E24\u4E2A\u89D2\u5EA6\u6216\u8F90\u89D2\u7684\u548C\u3002\u7279\u522B\u5730\uFF0C\u7528\u4E00\u4E2A\u6A21\u957F\u4E3A 1 \u7684\u590D\u6570\u76F8\u4E58\u5373\u4E3A\u4E00\u4E2A\u65CB\u8F6C\u3002"@zh , "In de wiskunde is het complexe vlak een geometrische weergave van de complexe getallen, bestaande uit een re\u00EBle as en loodrecht daarop geplaatst de imaginaire as. Het complexe vlak kan worden gezien als een aangepast cartesische vlak, waar het re\u00EBle deel van een complex getal wordt weergegeven door een verplaatsing langs de x-as en het imaginaire deel door een verplaatsing langs de y-as. Het complexe vlak wordt soms ook argandvlak genoemd, omdat dit wordt gebruikt in arganddiagrammen. Deze heten zo, omdat zij zijn genoemd naar Jean-Robert Argand, hoewel zij eerst zijn beschreven door de Noors-Deense landmeter en wiskundige Caspar Wessel. Wessels uiteenzetting werd in 1797 gepresenteerd aan de Deense Akademie. Argands werk werd in 1806 door hem zelf gepubliceerd. Arganddiagrammen worden vaak gebruikt om posities van de polen en nullen van een functie in de complexe ruimte te tekenen. Het concept van het complexe vlak staat een meetkundige interpretatie toe van de complexe getallen. De som van twee complexe getallen is hun vectori\u00EBle som en het product van twee complexe getallen kan het gemakkelijkst in poolco\u00F6rdinaten worden uitgedrukt, waar de grootte, of absolute waarde, van de twee poolco\u00F6rdinaten het product is van de twee absolute waarden, en waar de resulterende hoek van het product gelijk is aan de som van de twee hoeken. Om die reden worden arganddiagrammen vaak gebruikt om posities van de polen en nullen van een functie in de complexe ruimte te plotten. Een vermenigvuldiging met een complex getal met modulus 1 kan als een rotatie worden ge\u00EFnterpreteerd. Het complexe vlak wordt vaak gebruikt om fysische processen te visualiseren. Zo wordt een harmonische trilling gezien als een cirkelbeweging om de oorsprong in het complexe vlak. De projectie op de x-as is het re\u00EBle deel van de trilling, dat er in de tijd gezien uitziet als een sinus of cosinus."@nl , "\u03A3\u03C4\u03B1 \u039C\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AC, \u03C4\u03BF \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03CC \u03B5\u03C0\u03AF\u03C0\u03B5\u03B4\u03BF \u03AE z-\u03B5\u03C0\u03AF\u03C0\u03B5\u03B4\u03BF \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BC\u03AF\u03B1 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03B9\u03BA\u03AE \u03B1\u03BD\u03B1\u03C0\u03B1\u03C1\u03AC\u03C3\u03C4\u03B1\u03C3\u03B7 \u03C4\u03C9\u03BD \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03CE\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD ,\u03C4\u03BF \u03BF\u03C0\u03BF\u03AF\u03BF \u03B8\u03B5\u03C3\u03C0\u03AF\u03C3\u03C4\u03B7\u03BA\u03B5 \u03B1\u03C0\u03CC \u03C4\u03BF \u03C0\u03C1\u03B1\u03B3\u03BC\u03B1\u03C4\u03B9\u03BA\u03CC \u03AC\u03BE\u03BF\u03BD\u03B1 \u03BA\u03B1\u03B9 \u03C4\u03BF \u03BF\u03C1\u03B8\u03BF\u03B3\u03CE\u03BD\u03B9\u03BF 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\u03B5\u03C0\u03AF\u03C0\u03B5\u03B4\u03BF \u03BC\u03B5\u03C1\u03B9\u03BA\u03AD\u03C2 \u03C6\u03BF\u03C1\u03AD\u03C2 \u03BB\u03AD\u03B3\u03B5\u03C4\u03B1\u03B9 , \u03B5\u03C0\u03B5\u03B9\u03B4\u03AE \u03B1\u03C5\u03C4\u03CC \u03C7\u03C1\u03B7\u03C3\u03B9\u03BC\u03BF\u03C0\u03BF\u03B9\u03B5\u03AF\u03C4\u03B1\u03B9 \u03C3\u03B5 . \u0391\u03C5\u03C4\u03AC \u03C0\u03AE\u03C1\u03B1\u03BD \u03C4\u03BF \u03CC\u03BD\u03BF\u03BC\u03B1 \u03B1\u03C0\u03CC (1768\u20131822), \u03B1\u03BD \u03BA\u03B1\u03B9 \u03B1\u03C5\u03C4\u03AC \u03C0\u03C1\u03CE\u03C4\u03B1 \u03C0\u03B5\u03C1\u03B9\u03B3\u03C1\u03AC\u03C6\u03C4\u03B7\u03BA\u03B1\u03BD \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD \u0394\u03B1\u03BD\u03CC \u03C4\u03BF\u03C0\u03BF\u03B3\u03C1\u03AC\u03C6\u03BF \u03BA\u03B1\u03B9 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03CC (1745\u20131818).\u03A4\u03B1 \u03B4\u03B9\u03B1\u03B3\u03C1\u03AC\u03BC\u03BC\u03B1\u03C4\u03B1 \u03C4\u03BF\u03C5 Argand \u03C7\u03C1\u03B7\u03C3\u03B9\u03BC\u03BF\u03C0\u03BF\u03B9\u03BF\u03CD\u03BD\u03C4\u03B1\u03B9 \u03C3\u03C5\u03C7\u03BD\u03AC \u03B3\u03B9\u03B1 \u03C4\u03BF\u03BD \u03C3\u03C7\u03B5\u03B4\u03B9\u03B1\u03C3\u03BC\u03CC \u03C4\u03C9\u03BD \u03B8\u03AD\u03C3\u03B5\u03C9\u03BD \u03C4\u03C9\u03BD \u03C0\u03CC\u03BB\u03C9\u03BD \u03BA\u03B1\u03B9 \u03C4\u03C9\u03BD \u03BC\u03B7\u03B4\u03B5\u03BD\u03B9\u03BA\u03CE\u03BD \u03BC\u03B9\u03B1\u03C2 \u03C3\u03C5\u03BD\u03AC\u03C1\u03C4\u03B7\u03C3\u03B7\u03C2 \u03C3\u03C4\u03BF \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03CC \u03B5\u03C0\u03AF\u03C0\u03B5\u03B4\u03BF."@el ; dbo:wikiPageWikiLink dbc:Classical_control_theory , , dbr:Complex_analysis , dbr:Control_theory , , dbr:Residue_theorem , dbr:Even_and_odd_functions , , dbc:Complex_analysis , dbr:Zeros_and_poles , dbr:Analytic_function , dbr:Nyquist_plot , , dbr:Angle , dbr:Caspar_Wessel , dbr:Nyquist_stability_criterion , dbr:Bijection , dbr:Split-complex_plane , , , dbr:Complex_coordinate_space , , dbr:Power_series , dbr:Domain_of_a_function , dbr:Real_number , dbr:Dual_number , , dbr:Infinite_product , dbr:Topology , dbr:Inverse_trigonometric_function , dbr:Real_number_line , dbr:Uniform_convergence , dbr:In-phase_and_quadrature_components , dbr:Split-complex_number , dbr:Algebras_over_a_field , dbr:Mathematics , dbr:Quadratic_space , dbr:Euclidean_space , dbr:Multiplication , dbr:Sphere , dbr:Constellation_diagram , dbr:Composition_algebra , dbr:Discrete-time , dbr:Polar_coordinates , dbr:Unit_circle , dbr:Proof_that_holomorphic_functions_are_analytic , dbr:Meromorphic_function , dbr:Transfer_function , dbc:Complex_numbers , dbr:S_plane , , , dbr:Generalized_continued_fraction , dbr:Absolute_value , dbr:Convergence_problem , dbr:Riemann_zeta_function , dbr:Orientable , dbr:Jean-Robert_Argand , , dbr:Riemann_sphere , dbr:Quadratic_form , , dbr:Real_line , dbr:Minkowski_space , dbr:Z-transform , , , dbr:Point_at_infinity , dbr:Branch_point , dbr:Complex_number , dbr:Addition , dbr:Range_of_a_function , dbr:Imaginary_unit , dbr:Cartesian_coordinate_system , dbr:Imaginary_number , dbr:Radian , dbr:Line_integral , dbr:Inner_product , dbr:Laplace_transform , , , dbr:Gamma_function , dbr:Exponential_function , dbr:Countable_set , dbr:S-plane , dbr:Holomorphic_function . @prefix dbp: . @prefix dbt: . dbr:Complex_plane dbp:wikiPageUsesTemplate dbt:Section_link , dbt:Complex_numbers , , dbt:Complex_analysis_sidebar , dbt:ISBN , dbt:See_also , dbt:Short_description , dbt:Refn , dbt:Commons_category , dbt:Abs , dbt:Reflist , , dbt:Math , dbt:Main , dbt:MathWorld , dbt:Mvar , dbt:About , dbt:Clear , dbt:Cite_book ; dbo:thumbnail ; dbo:wikiPageRevisionID 1124288596 . @prefix ns11: . dbr:Complex_plane dbo:wikiPageExternalLink ns11:essai-sur-une-maniere-de-representer-des-quantites-imaginaires-dans-les-cons . @prefix ns12: . dbr:Complex_plane dbo:wikiPageExternalLink ns12:complexvariables00flan . @prefix xsd: . dbr:Complex_plane 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