{"id":181,"date":"2023-07-15T12:37:30","date_gmt":"2023-07-15T12:37:30","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e8%a4%87%e7%b4%a0%e6%95%b0%e3%81%ae%e7%b4%af%e4%b9%97\/"},"modified":"2023-07-15T12:37:30","modified_gmt":"2023-07-15T12:37:30","slug":"%e8%a4%87%e7%b4%a0%e6%95%b0%e3%81%ae%e7%b4%af%e4%b9%97","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e8%a4%87%e7%b4%a0%e6%95%b0%e3%81%ae%e7%b4%af%e4%b9%97\/","title":{"rendered":"\u8907\u7d20\u6570\u306e\u7d2f\u4e57"},"content":{"rendered":"<p>\u6b63\u3057\u3044\u65b9\u6cd5\u3092\u77e5\u3063\u3066\u3044\u308c\u3070\u3001<strong>\u8907\u7d20\u6570\u306e\u7d2f\u4e57<\/strong>\u3092\u89e3\u304f\u3053\u3068\u306f\u975e\u5e38\u306b\u7c21\u5358\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u4e8c\u9805\u5f62\u5f0f\u3001\u6975\u5f62\u5f0f\u3001\u4e09\u89d2\u5f62\u5f0f\u306e\u8907\u7d20\u6570\u306e 3 \u3064\u306e\u65b9\u6cd5\u3067\u8907\u7d20\u7d2f\u4e57\u3092\u89e3\u304f\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span id=\"Como_se_resuelve_la_potencia_de_un_numero_complejo\">\u8907\u7d20\u6570\u306e\u7d2f\u4e57\u3092\u89e3\u304f\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3088\u3044\u3067\u3059\u304b?<\/span><\/h2>\n<p>\u5192\u982d\u3067\u8ff0\u3079\u305f\u3088\u3046\u306b\u3001\u8907\u96d1\u306a\u6a29\u9650\u3092\u4f7f\u7528\u3057\u3066\u52d5\u4f5c\u3059\u308b\u5834\u5408\u30013 \u3064\u306e\u72b6\u6cc1\u304c\u767a\u751f\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u6700\u521d\u306e\u6700\u3082\u5358\u7d14\u306a\u65b9\u6cd5\u306f<strong>\u3001\u6570\u5024\u304c\u6975\u5f62\u5f0f\u3067<\/strong>\u4e0e\u3048\u3089\u308c\u308b\u5834\u5408\u3067\u3059\u3002 2 \u756a\u76ee\u306f\u4e8c\u9805\u5f62\u5f0f\u3067\u6570\u5024\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u4e09\u756a\u76ee\u306f\u4e09\u89d2\u5f62\u5f0f\u3067\u6570\u5024\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3067\u3059\u3002<\/p>\n<p>\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u6975\u5f62\u5f0f\u306e\u8907\u5408\u4f53\u3092\u64cd\u4f5c\u3059\u308b\u3068\u3001\u6f14\u7fd2\u3092\u3088\u308a\u8fc5\u901f\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u554f\u984c\u306e\u6570\u5024\u3092\u6975\u5f62\u5f0f\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u5b9f\u969b\u306b\u306f\u3001\u3069\u306e\u65b9\u6cd5\u3082<strong>\u7c21\u5358\u306b\u89e3\u6c7a\u3067\u304d<\/strong>\u307e\u3059\u3002\u305d\u3046\u306f\u8a00\u3063\u3066\u3082\u3001\u3059\u3079\u3066\u306e\u30b1\u30fc\u30b9\u304c\u3069\u306e\u3088\u3046\u306b\u89e3\u6c7a\u3055\u308c\u308b\u304b\u3092\u8aac\u660e\u3057\u3001\u6f14\u7fd2\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span id=\"Potencias_de_numeros_complejos_en_forma_polar\">\u6975\u5f62\u5f0f\u306e\u8907\u7d20\u6570\u306e\u3079\u304d\u4e57<\/span><\/h2>\n<p><strong>\u8907\u7d20\u7d2f\u4e57\u3092\u6975\u5f62\u5f0f\u3067<\/strong>\u89e3\u304d\u305f\u3044\u3068\u304d\u306f\u3001\u5358\u7d14\u306b\u4fc2\u6570\u3092 any \u306b\u4e0a\u3052\u3001\u5f15\u6570\u306b n \u3092\u4e57\u7b97\u3057\u307e\u3059\u3002\u6570\u5b66\u7684\u306b\u8868\u73fe\u3059\u308b\u3068\u3001\u6b21\u306e\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"184\" height=\"27\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/calculer-les-puissances-des-nombres-complexes.webp\" data-src=\"\" alt=\"\u8907\u7d20\u6570\u306e\u3079\u304d\u4e57\u3092\u8a08\u7b97\u3059\u308b\" class=\"wp-image-11376 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4ee5\u4e0b\u306b\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u793a\u3057\u307e\u3059\u306e\u3067\u3001\u81ea\u5206\u3067\u89e3\u6c7a\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"73\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-sur-les-puissances-des-nombres-complexes.webp\" data-src=\"\" alt=\"\u8907\u7d20\u6570\u306e\u7d2f\u4e57\u306e\u6f14\u7fd2\" class=\"wp-image-11377 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>\u624b\u9806\u306f\u975e\u5e38\u306b\u7c21\u5358\u3067\u3059\u3002\u4e0a\u3067\u30b3\u30e1\u30f3\u30c8\u3057\u305f\u5f0f\u3092\u9069\u7528\u3059\u308b\u3060\u3051\u3067\u3001\u7d50\u679c\u306f\u3059\u3067\u306b\u51fa\u3066\u3044\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"258\" height=\"149\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/pouvoirs-complexes.webp\" data-src=\"\" alt=\"\u8907\u96d1\u306a\u529b\" class=\"wp-image-11378 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"su-expand-link su-expand-link-more\" style=\"text-align:center\">\u89e3\u6c7a\u7b56\u3092\u793a\u3059<\/div>\n<div class=\"su-expand-link su-expand-link-less\" style=\"text-align:center\">\u8868\u793a\u3092\u5c11\u306a\u304f\u3059\u308b<\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span id=\"Potencias_de_numeros_complejos_en_forma_binomica\">\u4e8c\u9805\u5f62\u5f0f\u306e\u8907\u7d20\u6570\u306e\u3079\u304d\u4e57<\/span><\/h2>\n<p>\u4e00\u65b9\u3001<strong>\u4e8c\u9805\u5f62\u5f0f\u3067\u8907\u7d20\u7d2f\u4e57<\/strong>\u3092\u89e3\u304d\u305f\u3044\u5834\u5408\u306f\u30012 \u3064\u306e\u7570\u306a\u308b\u65b9\u6cd5\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002 1 \u3064\u76ee\u306f\u3001\u300c\u4ee3\u6570\u7684\u300d\u65b9\u6cd5\u3067\u3079\u304d\u4e57\u3092\u89e3\u304f\u3053\u3068\u3092\u6271\u3044\u307e\u3059 (i \u304c\u5909\u6570\u3067\u3042\u308b\u304b\u306e\u3088\u3046\u306b\u89e3\u6c7a\u3057\u307e\u3059)\u3002 2 \u756a\u76ee\u306e\u30b7\u30b9\u30c6\u30e0\u306f\u3001\u4e8c\u9805\u5f62\u5f0f\u3092\u6975\u5f62\u5f0f\u306b\u5909\u63db\u3057\u3066\u304b\u3089\u3001\u524d\u306e\u624b\u9806\u306b\u5f93\u3046\u3082\u306e\u3067\u3059\u3002<\/p>\n<p>\u4e8c\u9805\u5f62\u5f0f\u304b\u3089\u6975\u5f62\u5f0f\u306b\u79fb\u884c\u3059\u308b\u65b9\u6cd5\u304c\u308f\u304b\u3089\u306a\u3044\u5834\u5408\u306f\u3001<a href=\"https:\/\/mathority.org\/ja\/\u8907\u7d20\u6570\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u8907\u7d20\u6570<\/a>\u306b\u95a2\u3059\u308b\u8a18\u4e8b\u3067\u308f\u304b\u308a\u3084\u3059\u304f\u8aac\u660e\u3057\u3066\u3044\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u3053\u3053\u3067\u306f\u4f8b\u3092\u4f7f\u3063\u3066\u7c21\u5358\u306b\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<p><strong>\u6b21\u306e\u8907\u7d20\u7d2f\u4e57\u3092\u89e3\u3044\u3066\u307f\u3066\u304f\u3060\u3055\u3044: (2 + 3i) <sup>2<\/sup> \u3002<\/strong> <\/p>\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>\u307e\u305a\u3001\u3053\u306e\u6f14\u7b97\u304c\u300c\u4ee3\u6570\u7684\u624b\u6cd5\u300d\u306b\u3088\u3063\u3066\u3069\u306e\u3088\u3046\u306b\u89e3\u6c7a\u3055\u308c\u308b\u304b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u3053\u306e\u7279\u5b9a\u306e\u30b1\u30fc\u30b9\u3067\u306f\u3001<a href=\"https:\/\/mathority.org\/ja\/\u6ce8\u76ee\u306e\u88fd\u54c1\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6ce8\u76ee\u3059\u3079\u304d\u7a4d<\/a>(a + b) <sup>2<\/sup> = a <sup>2<\/sup> + 2ab + b <sup>2<\/sup>\u3092\u9069\u7528\u3067\u304d\u307e\u3059\u3002<\/p>\n<p class=\"has-text-align-center\"> <strong>(2 + 3i) <sup>2<\/sup><\/strong> = 2 <sup>2<\/sup> + 2 2 3i + 3i <sup>2<\/sup><\/p>\n<p>\u6b21\u306b\u3001\u64cd\u4f5c\u3068\u7c21\u7d20\u5316\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n<p class=\"has-text-align-center\"> = 4 \u2013 9 + 12i = -5 + 12i<\/p>\n<p>\u6b21\u306b\u30012 \u756a\u76ee\u306e\u65b9\u6cd5\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6570\u5024\u3092\u6975\u5f62\u5f0f\u3067\u8868\u73fe\u3059\u308b\u3053\u3068\u304b\u3089\u59cb\u3081\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"272\" height=\"89\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/conversion-des-nombres-complexes.webp\" data-src=\"\" alt=\"\u8907\u7d20\u6570\u306e\u5909\u63db\" class=\"wp-image-11393 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b21\u306b\u3001\u6700\u521d\u306b\u8aac\u660e\u3057\u305f\u5f0f\u306b\u5f93\u3063\u3066\u64cd\u4f5c\u3057\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"286\" height=\"34\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/puissance-complexe.webp\" data-src=\"\" alt=\"\u8907\u96d1\u306a\u529b\" class=\"wp-image-11394 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u305d\u3057\u3066\u6700\u7d42\u7684\u306b\u306f\u3001\u6975\u5f62\u5f0f\u3067\u306e\u307f\u540c\u3058\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u540c\u3058\u6570\u5024\u3067\u306f\u306a\u3044\u3068\u601d\u308f\u308c\u308b\u5834\u5408\u306f\u3001\u81ea\u5206\u3067\u5909\u63db\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002\u3082\u3061\u308d\u3093\u3001\u5f97\u3089\u308c\u305f\u4e8c\u9805\u5f62\u5f0f\u306e\u7d50\u679c\u306e\u5f15\u6570\u306f<strong>\u7b2c 2 \u8c61\u9650\u306b\u3042\u308b<\/strong>\u3053\u3068\u306b\u7559\u610f\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u89d2\u5ea6\u306b \u03c0 \u3092\u8ffd\u52a0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<div class=\"su-expand-link su-expand-link-more\" style=\"text-align:center\">\u89e3\u6c7a\u7b56\u3092\u793a\u3059<\/div>\n<div class=\"su-expand-link su-expand-link-less\" style=\"text-align:center\">\u8868\u793a\u3092\u5c11\u306a\u304f\u3059\u308b<\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span id=\"Potencias_de_numeros_complejos_en_forma_trigonometrica\">\u4e09\u89d2\u95a2\u6570\u5f62\u5f0f\u306e\u8907\u7d20\u6570\u306e\u3079\u304d\u4e57<\/span><\/h2>\n<p>\u6700\u5f8c\u306b\u3001<strong>\u4e09\u89d2\u95a2\u6570\u5f62\u5f0f\u3067\u8907\u7d20\u7d2f\u4e57<\/strong>\u3092\u89e3\u304d\u305f\u3044\u3068\u304d\u306f\u3001\u3088\u304f\u77e5\u3089\u308c\u305f\u30c9 \u30e2\u30a2\u30d6\u30eb\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u304b\u308c\u3066\u3044\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"224\" height=\"66\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/la-formule-de-moivre.webp\" data-src=\"\" alt=\"\u30e2\u30a2\u30d6\u30eb\u306e\u516c\u5f0f\" class=\"wp-image-11380 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u3053\u306e\u516c\u5f0f\u3092\u7406\u89e3\u3057\u305f\u4e0a\u3067\u3001\u6b21\u306e\u6f14\u7fd2\u3092\u89e3\u3044\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"213\" height=\"100\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-de-pouvoirs-complexes.webp\" data-src=\"\" alt=\"\u8907\u96d1\u306a\u6a29\u9650\u306e\u884c\u4f7f\" class=\"wp-image-11381 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>\u30c9\u30fb\u30e2\u30a2\u30d6\u30eb\u306e\u516c\u5f0f\u3092\u9069\u7528\u3059\u308b\u3060\u3051\u3067\u3001\u3059\u3079\u3066\u306e\u7df4\u7fd2\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"369\" height=\"149\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/puissance-des-nombres-complexes-sous-forme-trigonometrique.webp\" data-src=\"\" alt=\"\u4e09\u89d2\u95a2\u6570\u5f62\u5f0f\u306e\u8907\u7d20\u6570\u306e\u7d2f\u4e57\" class=\"wp-image-11382 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u305f\u3060\u3057\u3001\u6700\u5f8c\u306e\u30b1\u30fc\u30b9\u306f\u5909\u6570\u3067\u306f\u306a\u304f\u6570\u5024\u306e\u89d2\u5ea6\u3092\u6301\u3063\u3066\u3044\u308b\u305f\u3081\u3001\u591a\u5c11\u7570\u306a\u308a\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"292\" height=\"150\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/calculer-des-puissances-avec-des-nombres-complexes.webp\" data-src=\"\" alt=\"\u8907\u7d20\u6570\u3092\u4f7f\u3063\u3066\u3079\u304d\u4e57\u3092\u8a08\u7b97\u3059\u308b\" class=\"wp-image-11383 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"su-expand-link su-expand-link-more\" style=\"text-align:center\">\u89e3\u6c7a\u7b56\u3092\u793a\u3059<\/div>\n<div class=\"su-expand-link su-expand-link-less\" style=\"text-align:center\">\u8868\u793a\u3092\u5c11\u306a\u304f\u3059\u308b<\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span id=\"Mas_sobre_las_potencias_complejas\">\u8907\u7d20\u6570\u30d1\u30ef\u30fc\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u5b66\u3076<\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/mathority.org\/ja\/\u8907\u7d20\u6570\/\" 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\u3064\u306e\u65b9\u6cd5\u3067\u8907\u7d20\u7d2f\u4e57\u3092\u89e3\u304f\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002 \u8907\u7d20\u6570\u306e\u7d2f\u4e57\u3092\u89e3\u304f\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3088\u3044\u3067\u3059\u304b &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e8%a4%87%e7%b4%a0%e6%95%b0%e3%81%ae%e7%b4%af%e4%b9%97\/\"> <span class=\"screen-reader-text\">\u8907\u7d20\u6570\u306e\u7d2f\u4e57<\/span> \u3082\u3063\u3068\u8aad\u3080 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