{"id":179,"date":"2023-07-15T13:24:09","date_gmt":"2023-07-15T13:24:09","guid":{"rendered":"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/"},"modified":"2023-07-15T13:24:09","modified_gmt":"2023-07-15T13:24:09","slug":"raizes-de-numeros-complexos","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/","title":{"rendered":"Ra\u00edzes de n\u00fameros complexos"},"content":{"rendered":"<p>Calcular <strong>as ra\u00edzes de n\u00fameros complexos<\/strong> \u00e9 bastante simples. Bem, depois de entender o procedimento, ele se torna bastante repetitivo. A seguir explicaremos e daremos um exemplo, para que voc\u00ea aprenda como aplic\u00e1-lo em exerc\u00edcios reais.<\/p>\n<h2 class=\"wp-block-heading\"> <span id=\"Raices_enesimas_de_numeros_complejos\">en\u00e9simas ra\u00edzes de n\u00fameros complexos<\/span><\/h2>\n<p> O conceito de raiz en\u00e9sima equivale a dizer raiz de ordem n, portanto, o mesmo m\u00e9todo \u00e9 usado para calcular a raiz quadrada e a raiz quinta de um n\u00famero complexo. \u00c9 claro que o n\u00famero de solu\u00e7\u00f5es mudar\u00e1 dependendo desta ordem.<\/p>\n<p> Por exemplo, se calcularmos a raiz quarta de um complexo, obteremos 4 solu\u00e7\u00f5es diferentes. E se expressarmos no <a href=\"https:\/\/mathority.org\/pt\/plano-complexo\/\" target=\"_blank\" rel=\"noreferrer noopener\">plano complexo<\/a> , vemos que se forma um pol\u00edgono regular de 4 lados, centrado na origem do plano. Esta \u00e9 uma propriedade muito interessante, que veremos em detalhes mais adiante (na se\u00e7\u00e3o de exemplos).<\/p>\n<p> Agora que esclarecemos esse conceito, veremos como calcular a raiz de um n\u00famero complexo na forma polar (usar esta nota\u00e7\u00e3o \u00e9 a mais confort\u00e1vel para resolver uma raiz). Simplesmente, voc\u00ea precisa calcular a raiz do m\u00f3dulo e expressar o argumento em termos de n. Em outras palavras, a raiz do seguinte n\u00famero complexo (z): <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"72\" height=\"29\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-sous-forme-polaire.webp\" data-src=\"\" alt=\"n\u00famero na forma polar\" class=\"wp-image-11307 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Esses valores para calcular:<\/p>\n<ul>\n<li> <strong>M\u00f3dulo:<\/strong> A en\u00e9sima raiz do m\u00f3dulo inicial.<\/li>\n<li> <strong>Argumento:<\/strong> Adicione 2\u03c0k em radianos ou 360k em graus ao argumento e divida por n.<\/li>\n<\/ul>\n<p> Matematicamente, para calcular o m\u00f3dulo e o argumento usamos as duas f\u00f3rmulas a seguir: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"114\" height=\"89\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/racines-des-nombres-complexes.webp\" data-src=\"\" alt=\"Ra\u00edzes de n\u00fameros complexos\" class=\"wp-image-11371 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Onde, k = 0, 1, 2,\u2026, n-1.<\/p>\n<p> E, portanto, expressamos o resultado da seguinte forma: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"84\" height=\"43\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/calculer-la-racine-nieme-dun-nombre-complexe.webp\" data-src=\"\" alt=\"Calcule a en\u00e9sima raiz de um n\u00famero complexo\" class=\"wp-image-11347 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Para ficar claro, as n solu\u00e7\u00f5es que obteremos resolvendo esta raiz ser\u00e3o formadas pelo mesmo m\u00f3dulo e n argumentos diferentes.<\/p>\n<h2 class=\"wp-block-heading\"> <span id=\"Ejemplos_del_calculo_de_raices_enesimas_de_complejos\">Exemplos de c\u00e1lculo de en\u00e9simas ra\u00edzes de complexos<\/span><\/h2>\n<p> Veremos agora alguns exemplos de c\u00e1lculo das ra\u00edzes en\u00e9simas de n\u00fameros complexos. Recomendamos que voc\u00ea tente resolv\u00ea-los sozinho e, quando terminar, verifique a corre\u00e7\u00e3o. N\u00e3o esque\u00e7a que o m\u00e9todo \u00e9 explicado logo acima.<\/p>\n<p> <strong>Encontre a terceira raiz do n\u00famero complexo: 1 + <strong>i<\/strong> \u221a3<\/strong> . <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"89\" height=\"55\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-de-racines-complexes.webp\" data-src=\"\" alt=\"Exerc\u00edcio de ra\u00edzes complexas\" class=\"wp-image-11349 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"su-expand su-expand-collapsed su-expand-link-style-button\" data-height=\"0\">\n<div class=\"su-expand-content su-u-trim\" style=\"color:#333333;max-height:0px;overflow:hidden\">\n<p> <strong>ATEN\u00c7\u00c3O:<\/strong> Resolveremos este exerc\u00edcio usando radianos e n\u00e3o graus.<\/p>\n<p> Como podemos ver, o n\u00famero \u00e9 expresso na forma binomial, portanto o primeiro passo deve ser express\u00e1-lo na forma polar. Se voc\u00ea n\u00e3o sabe como fazer isso, recomendamos a leitura de nosso artigo sobre <a href=\"https:\/\/mathority.org\/pt\/numeros-complexos\/\" target=\"_blank\" rel=\"noreferrer noopener\">n\u00fameros complexos<\/a> , no qual discutimos detalhadamente esse tema. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"209\" height=\"116\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/racine-dun-nombre-polaire.webp\" data-src=\"\" alt=\"raiz de um n\u00famero polar\" class=\"wp-image-11329 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Assim que tivermos o n\u00famero na forma polar, basta usar as f\u00f3rmulas anteriores para calcular o novo m\u00f3dulo e os diferentes argumentos. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"303\" height=\"175\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-calcul-des-racines-dun-nombre-complexe.webp\" data-src=\"\" alt=\"Exemplo de c\u00e1lculo das ra\u00edzes de um n\u00famero complexo\" class=\"wp-image-11330 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> E, finalmente, expressamo-lo na forma polar. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"94\" height=\"143\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/racine-dun-exercice-sur-les-nombres-complexes.webp\" data-src=\"\" alt=\"Raiz de um exerc\u00edcio sobre n\u00fameros complexos\" class=\"wp-image-11331 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Al\u00e9m disso, podemos escrev\u00ea-lo na forma trigonom\u00e9trica e binomial: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"308\" height=\"332\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/racines-complexes.webp\" data-src=\"\" alt=\"ra\u00edzes complexas\" class=\"wp-image-11332 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> E por fim, representamos no plano complexo: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-medium\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"472\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/representation-graphique-racines-complexes.webp\" data-src=\"\" alt=\"Representa\u00e7\u00e3o gr\u00e1fica Ra\u00edzes complexas\" class=\"wp-image-11353 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2023\/02\/Representacion-grafica-Raices-complejas-500x472.png 500w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2023\/02\/Representacion-grafica-Raices-complejas.png 619w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<\/div>\n<div class=\"su-expand-link su-expand-link-more\" style=\"text-align:center\"> mostre a solu\u00e7\u00e3o<\/div>\n<div class=\"su-expand-link su-expand-link-less\" style=\"text-align:center\"> Mostre menos<\/div>\n<\/div>\n<p> <strong>Encontre a quarta raiz do n\u00famero complexo: 3+i <strong>\u221a<\/strong> 3<\/strong> . <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"87\" height=\"47\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-racines-complexes.webp\" data-src=\"\" alt=\"Exemplo de ra\u00edzes complexas\" class=\"wp-image-11350 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"su-expand su-expand-collapsed su-expand-link-style-button\" data-height=\"0\">\n<div class=\"su-expand-content su-u-trim\" style=\"color:#333333;max-height:0px;overflow:hidden\">\n<p> <strong>ATEN\u00c7\u00c3O:<\/strong> Resolvemos este exerc\u00edcio usando radianos e n\u00e3o graus.<\/p>\n<p> Como antes, come\u00e7amos convertendo a forma binomial na forma polar. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"212\" height=\"115\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/binome-a-polaire.webp\" data-src=\"\" alt=\"binomial para polar\" class=\"wp-image-11342 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Em seguida, aplicamos as f\u00f3rmulas para calcular o novo m\u00f3dulo e argumentos. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"302\" height=\"232\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/calcul-des-racines-complexes.webp\" data-src=\"\" alt=\"C\u00e1lculo de ra\u00edzes complexas\" class=\"wp-image-11343 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Expressamos o resultado na forma polar. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"101\" height=\"199\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/racines-des-nombres-complexes-sous-forme-polaire.webp\" data-src=\"\" alt=\"Ra\u00edzes de n\u00fameros complexos na forma polar\" class=\"wp-image-11344 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Em seguida, expressamos o resultado na forma trigonom\u00e9trica e binomial. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"335\" height=\"458\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/racines-de-nombres-complexes-sous-forme-binomiale.webp\" data-src=\"\" alt=\"Ra\u00edzes de n\u00fameros complexos na forma binomial\" class=\"wp-image-11345 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> E, finalmente, representamos graficamente as solu\u00e7\u00f5es no plano complexo. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-medium\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"474\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/tracer-des-racines-complexes.webp\" data-src=\"\" alt=\"Desenhando ra\u00edzes complexas\" class=\"wp-image-11356 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2023\/02\/Graficar-raices-complejas-500x474.png 500w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2023\/02\/Graficar-raices-complejas.png 613w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<\/div>\n<div class=\"su-expand-link su-expand-link-more\" style=\"text-align:center\"> mostre a solu\u00e7\u00e3o<\/div>\n<div class=\"su-expand-link su-expand-link-less\" style=\"text-align:center\"> Mostre menos<\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"> <span id=\"Mas_sobre_raices_de_numeros_complejos\">Aprenda sobre as ra\u00edzes dos n\u00fameros complexos<\/span><\/h2>\n<ul>\n<li> <a href=\"https:\/\/mathority.org\/pt\/numeros-complexos\/\" target=\"_blank\" rel=\"noreferrer noopener\">N\u00fameros complexos<\/a><\/li>\n<li> <a href=\"https:\/\/mathority.org\/pt\" target=\"_blank\" rel=\"noreferrer noopener\">Opera\u00e7\u00f5es em n\u00fameros complexos<\/a><\/li>\n<li> <a href=\"https:\/\/mathority.org\/pt\/potencias-de-numeros-complexos\/\" target=\"_blank\" rel=\"noreferrer noopener\">poderes complexos<\/a><\/li>\n<li> <a href=\"https:\/\/mathority.org\/pt\/propriedades-de-numeros-complexos\/\" target=\"_blank\" rel=\"noreferrer noopener\">Propriedades de n\u00fameros complexos<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calcular as ra\u00edzes de n\u00fameros complexos \u00e9 bastante simples. Bem, depois de entender o procedimento, ele se torna bastante repetitivo. A seguir explicaremos e daremos um exemplo, para que voc\u00ea aprenda como aplic\u00e1-lo em exerc\u00edcios reais. en\u00e9simas ra\u00edzes de n\u00fameros complexos O conceito de raiz en\u00e9sima equivale a dizer raiz de ordem n, portanto, o &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/\"> <span class=\"screen-reader-text\">Ra\u00edzes de n\u00fameros complexos<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[32,14],"tags":[],"class_list":["post-179","post","type-post","status-publish","format-standard","hentry","category-aritmetica","category-explicacoes-matematicas"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Ra\u00edzes de n\u00fameros complexos - Matoridade<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ra\u00edzes de n\u00fameros complexos - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Calcular as ra\u00edzes de n\u00fameros complexos \u00e9 bastante simples. Bem, depois de entender o procedimento, ele se torna bastante repetitivo. A seguir explicaremos e daremos um exemplo, para que voc\u00ea aprenda como aplic\u00e1-lo em exerc\u00edcios reais. en\u00e9simas ra\u00edzes de n\u00fameros complexos O conceito de raiz en\u00e9sima equivale a dizer raiz de ordem n, portanto, o &hellip; Ra\u00edzes de n\u00fameros complexos Leia mais &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-15T13:24:09+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-sous-forme-polaire.webp\" \/>\n<meta name=\"author\" content=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Ra\u00edzes de n\u00fameros complexos\",\"datePublished\":\"2023-07-15T13:24:09+00:00\",\"dateModified\":\"2023-07-15T13:24:09+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/\"},\"wordCount\":564,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"Aritm\u00e9tica\",\"Explica\u00e7\u00f5es matem\u00e1ticas\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/\",\"url\":\"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/\",\"name\":\"Ra\u00edzes de n\u00fameros complexos - 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Matoridade","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/","og_locale":"pt_BR","og_type":"article","og_title":"Ra\u00edzes de n\u00fameros complexos - Matoridade","og_description":"Calcular as ra\u00edzes de n\u00fameros complexos \u00e9 bastante simples. Bem, depois de entender o procedimento, ele se torna bastante repetitivo. A seguir explicaremos e daremos um exemplo, para que voc\u00ea aprenda como aplic\u00e1-lo em exerc\u00edcios reais. en\u00e9simas ra\u00edzes de n\u00fameros complexos O conceito de raiz en\u00e9sima equivale a dizer raiz de ordem n, portanto, o &hellip; Ra\u00edzes de n\u00fameros complexos Leia mais &raquo;","og_url":"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/","article_published_time":"2023-07-15T13:24:09+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-sous-forme-polaire.webp"}],"author":"Equipe Mathoridade","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Equipe Mathoridade","Est. tempo de leitura":"3 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/"},"author":{"name":"Equipe Mathoridade","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00"},"headline":"Ra\u00edzes de n\u00fameros complexos","datePublished":"2023-07-15T13:24:09+00:00","dateModified":"2023-07-15T13:24:09+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/"},"wordCount":564,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"articleSection":["Aritm\u00e9tica","Explica\u00e7\u00f5es matem\u00e1ticas"],"inLanguage":"pt-BR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/","url":"https:\/\/mathority.org\/pt\/raizes-de-numeros-complexos\/","name":"Ra\u00edzes de n\u00fameros complexos - 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