{"id":2027,"date":"2021-12-11T10:04:57","date_gmt":"2021-12-11T01:04:57","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=2027"},"modified":"2021-12-11T10:06:32","modified_gmt":"2021-12-11T01:06:32","slug":"tbr202106","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tbr202106\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2021\uff1a\u7b2c6\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(i\\) \u3092\u865a\u6570\u5358\u4f4d\u3068\u3059\u308b.\r\n\u8907\u7d20\u6570\u5e73\u9762\u306b\u304a\u3044\u3066, \u8907\u7d20\u6570 \\(z\\) \u306e\u8868\u3059\u70b9 P \u3092 P \\((z)\\) \u307e\u305f\u306f\u70b9 \\(z\\) \u3068\u66f8\u304f.\r\n\\(\\omega = -\\dfrac{1}{2} +\\dfrac{\\sqrt{3}}{2} i\\) \u3068\u304a\u304d, \\(3\\) \u70b9 A \\((1)\\) , B \\(( \\omega )\\) , C \\(( \\omega^2 )\\) \u3092\u9802\u70b9\u3068\u3059\u308b \\(\\triangle \\text{ABC}\\) \u3092\u8003\u3048\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(\\triangle \\text{ABC}\\) \u306f\u6b63\u4e09\u89d2\u5f62\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u70b9 \\(z\\) \u304c\u8fba AC \u4e0a\u3092\u52d5\u304f\u3068\u304d, \u70b9 \\(-z\\) \u304c\u63cf\u304f\u56f3\u5f62\u3092\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u306b\u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n<li><p><strong>(3)<\/strong>\u3000\u70b9 \\(z\\) \u304c\u8fba AB \u4e0a\u3092\u52d5\u304f\u3068\u304d, \u70b9 \\(z^2\\) \u304c\u63cf\u304f\u56f3\u5f62\u3092 \\(E_1\\) \u3068\u3059\u308b.\r\n\u307e\u305f, \u70b9 \\(z\\) \u304c\u8fba AC \u4e0a\u3092\u52d5\u304f\u3068\u304d, \u70b9 \\(z^2\\) \u304c\u63cf\u304f\u56f3\u5f62\u3092 \\(E_2\\) \u3068\u3059\u308b.\r\n\\(E_1\\) \u3068 \\(E_2\\) \u306e\u5171\u6709\u70b9\u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\[\\begin{align}\r\n\\omega & = \\cos \\dfrac{2 \\pi}{3} +i \\sin \\dfrac{2 \\pi}{3} \\ , \\\\\r\n\\omega^2 & = \\cos \\dfrac{4 \\pi}{3} +i \\sin \\dfrac{4 \\pi}{3} = \\cos \\left( -\\dfrac{2 \\pi}{3} \\right) +i \\sin \\left( -\\dfrac{2 \\pi}{3} \\right)\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\n& \\text{OA} = \\text{OB} = \\text{OC} = 1 \\ , \\\\\r\n& \\angle \\text{AOB} = \\angle \\text{BOC} = \\angle \\text{COA} = \\dfrac{2 \\pi}{3}\r\n\\end{align}\\]\r\n\u3086\u3048\u306b, \\(2\\) \u8fba\u3068\u305d\u306e\u9593\u306e\u89d2\u304c\u305d\u308c\u305e\u308c\u7b49\u3057\u3044\u306e\u3067\r\n\\[\r\n\\triangle \\text{OAB} \\equiv \\triangle \\text{OBC} \\equiv \\triangle \\text{OCA}\r\n\\]\r\n\u3088\u3063\u3066, \\(\\text{AB} = \\text{BC} = \\text{CA}\\) \u306a\u306e\u3067, \\(\\triangle \\text{ABC}\\) \u306f\u6b63\u4e09\u89d2\u5f62.<\/p>\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\u70b9 \\(-z\\) \u306f\u70b9 \\(z\\) \u3068\u539f\u70b9\u306b\u3064\u3044\u3066\u5bfe\u79f0\u306a\u306e\u3067, \u63cf\u304f\u56f3\u5f62\u306f\u4e0b\u56f3\u5b9f\u7dda\u90e8.<\/p>\r\n<img decoding=\"async\" src=\"\/nyushi\/wp-content\/uploads\/tbr20210601.svg\" alt=\"tbr20210601\" class=\"aligncenter size-full\" \/>\r\n<p><strong>(3)<\/strong><\/p>\r\n<p>AB, AC \u4e0a\u3092\u52d5\u304f \\(z\\) \u3092\u305d\u308c\u305e\u308c \\(z_1 , z_2\\) \u3068\u304a\u304f\u3068 \\(E_1 , E_2\\) \u306e\u5171\u6709\u70b9\u3068\u306a\u308b\u306e\u306f\r\n\\[\\begin{align}\r\n{ z_1 }^2 & = { z_2 }^2 \\\\\r\n\\text{\u2234} \\quad z_1 & = \\pm z_2\r\n\\end{align}\\]\r\n<ul>\r\n<li><p>\\(z_1 = z_2\\) \u306e\u3068\u304d, AB \u3068 AC \u306e\u5171\u6709\u70b9\u306f A \u306a\u306e\u3067\r\n\\[\r\nz = 1\r\n\\]\r\n\u3053\u306e\u3068\u304d, \\(z^2 = 1\\) .<\/p><\/li>\r\n<li><p>\\(z_1 = -z_2\\) \u306e\u3068\u304d, <strong>(2)<\/strong> \u3067\u6c42\u3081\u305f\u56f3\u5f62\u3068 AB \u306e\u5171\u6709\u70b9\u306f \\(\\dfrac{i}{\\sqrt{3}}\\) \u306a\u306e\u3067\r\n\\[\r\nz = \\dfrac{i}{\\sqrt{3}}\r\n\\]\r\n\u3053\u306e\u3068\u304d, \\(z^2 = -\\dfrac{1}{3}\\) .<\/p><\/li>\r\n<\/ul>\r\n<p>\u3088\u3063\u3066, \u6c42\u3081\u308b\u5171\u6709\u70b9\u306f\r\n\\[\r\n\\underline{1 , -\\dfrac{1}{3}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(i\\) \u3092\u865a\u6570\u5358\u4f4d\u3068\u3059\u308b. \u8907\u7d20\u6570\u5e73\u9762\u306b\u304a\u3044\u3066, \u8907\u7d20\u6570 \\(z\\) \u306e\u8868\u3059\u70b9 P \u3092 P \\((z)\\) \u307e\u305f\u306f\u70b9 \\(z\\) \u3068\u66f8\u304f. \\(\\omega = -\\dfrac{1}{2} +\\dfrac{\\sqrt &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tbr202106\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[178],"tags":[144,165],"class_list":["post-2027","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2021","tag-tsukuba_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2027","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=2027"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2027\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=2027"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=2027"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=2027"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}