{"id":2033,"date":"2021-12-15T00:11:01","date_gmt":"2021-12-14T15:11:01","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=2033"},"modified":"2021-12-15T00:18:14","modified_gmt":"2021-12-14T15:18:14","slug":"wsr202103","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr202103\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52021\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\u8907\u7d20\u6570 \\(\\alpha = 2 +i\\) , \\(\\beta = -\\dfrac{1}{2} +i\\) \u306b\u5bfe\u5fdc\u3059\u308b\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u306e\u70b9\u3092 \\(\\text{A} ( \\alpha ) , \\text{B} ( \\beta )\\) \u3068\u3059\u308b.\r\n\u3053\u306e\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u306e\u70b9 \\(\\text{C} ( \\alpha^2 )\\) , \\(\\text{D} ( \\beta^2 )\\) \u3068\u539f\u70b9 O \u306e \\(3\\) \u70b9\u306f\u4e00\u76f4\u7dda\u4e0a\u306b\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u70b9 \\(\\text{P} (z)\\) \u304c\u76f4\u7dda AB \u4e0a\u3092\u52d5\u304f\u3068\u304d, \\(z^2\\) \u306e\u5b9f\u90e8\u3092 \\(x\\) , \u865a\u90e8\u3092 \\(y\\) \u3068\u3057\u3066,\r\n\u70b9 \\(\\text{Q} ( z^2 )\\) \u306e\u8ecc\u8de1\u3092 \\(x , y\\) \u306e\u65b9\u7a0b\u5f0f\u3067\u8868\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u70b9 \\(\\text{P} (z)\\) \u304c\u4e09\u89d2\u5f62 OAB \u306e\u5468\u304a\u3088\u3073\u5185\u90e8\u306b\u3042\u308b\u3068\u304d,\r\n\u70b9 \\(\\text{Q} ( z^2 )\\) \u5168\u4f53\u306e\u306a\u3059\u56f3\u5f62\u3092 \\(K\\) \u3068\u3059\u308b.\r\n\\(K\\) \u3092\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u306b\u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n

  4. (4)<\/strong>\u3000(3)<\/strong> \u306e\u56f3\u5f62 \\(K\\) \u306e\u9762\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \u6761\u4ef6\u3088\u308a\r\n\\[\\begin{align}\r\n\\alpha^2 & = 3 +4i \\ , \\\\\r\n\\beta^2 & = -\\dfrac{3}{4} -i = -\\dfrac{1}{4} \\alpha^2\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, O, C, D \u306f\u4e00\u76f4\u7dda\u4e0a\u306b\u3042\u308b.<\/p>\r\n

    (2)<\/strong><\/p>\r\n

    \\(z = u +i\\) \u3068\u8868\u305b\u308b.\r\n\\[\r\nz^2 = u^2 -1 +2u i\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\r\n\\left\\{ \\begin{array}{ll} x = u^2 -1 & ... [1] \\\\ y = 2u & ... [2] \\end{array} \\right.\r\n\\]\r\n[2] \u3088\u308a, \\(u = \\dfrac{y}{2}\\) \u3067, [1] \u306b\u4ee3\u5165\u3057\u3066\r\n\\[\r\nx = \\dfrac{y^2}{4} -1\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u8ecc\u8de1\u306e\u5f0f\u306f\r\n\\[\r\n\\underline{x = \\dfrac{y^2}{4} -1}\r\n\\]\r\n

    (3)<\/strong><\/p>\r\n

    \u7dda\u5206 AB \u4e0a\u3092 \\(z\\) \u304c\u52d5\u304f\u3068\u304d, (2)<\/strong> \u3067\u8003\u3048\u305f\u4e2d\u3067 \\(-\\dfrac{1}{2} \\leqq u \\leqq 2\\) \u306e\u7bc4\u56f2\u3092\u52d5\u304d,\r\n\\(z^2\\) \u306f \\(-1 \\leqq y \\leqq 4\\) \u306e\u7bc4\u56f2\u3092\u52d5\u304f.
    \r\n\\(z\\) \u304c \\(\\triangle \\text{OAB}\\) \u3092\u52d5\u304f\u3068\u304d, \u7dda\u5206 AB \u4e0a\u306e\u70b9 \\(z'\\) \u306b\u5bfe\u3057\u3066\r\n\\[\r\nz = k z' \\ ( 0 \\leqq k \\leqq 1 )\r\n\\]\r\n\u3068\u8868\u305b\u308b.\r\n\\[\r\nz^2 = k^2 {z'}^2 \\ , \\ 0 \\leqq k^2 \\leqq 1\r\n\\]\r\n\u306a\u306e\u3067, \u6c42\u3081\u308b\u56f3\u5f62\u306f, \u70b9 \\({z'}^2\\) \u306e\u8ecc\u8de1\r\n\\[\r\nx = \\dfrac{y^2}{4} -1 \\ ( -1 \\leqq y \\leqq 4 )\r\n\\]\r\n\u3068\u539f\u70b9\u3092\u7d50\u3076\u7dda\u5206\u5168\u4f53\u304c\u8868\u3059\u9818\u57df\u3067, \u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u3092\u542b\u3080\uff09.<\/p>\r\n\"wsr20210301\"\r\n

    (4)<\/strong><\/p>\r\n

    \u76f4\u7dda CD \u306e\u5f0f\u306f \\(x = \\dfrac{3}{4} y\\) \u306a\u306e\u3067, \u6c42\u3081\u308b\u9762\u7a4d \\(S\\) \u306f\r\n\\[\\begin{align}\r\nS & = \\displaystyle\\int _ {-1}^{4} \\left( \\dfrac{3}{4} y -\\dfrac{y^2}{4} +1 \\right) \\, dy \\\\\r\n& = -\\dfrac{1}{4} \\displaystyle\\int _ {-1}^{4} (x+1) (x-4) \\, dy \\\\\r\n& = \\dfrac{1}{4} \\cdot \\dfrac{1}{6} ( 4+1 )^3 \\\\\r\n& = \\underline{\\dfrac{125}{24}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u8907\u7d20\u6570 \\(\\alpha = 2 +i\\) , \\(\\beta = -\\dfrac{1}{2} +i\\) \u306b\u5bfe\u5fdc\u3059\u308b\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u306e\u70b9\u3092 \\(\\text{A} ( \\alpha ) , \\text{B} ( \\beta ) … \u7d9a\u304d\u3092\u8aad\u3080 →<\/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":[177],"tags":[147,165],"class_list":["post-2033","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2021","tag-waseda_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2033","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=2033"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2033\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=2033"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=2033"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=2033"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}