{"id":156183,"date":"2023-08-29T14:08:38","date_gmt":"2023-08-29T08:38:38","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=156183"},"modified":"2023-08-29T14:13:53","modified_gmt":"2023-08-29T08:43:53","slug":"a-complex-function-%f0%9d%91%93%f0%9d%91%a7-%f0%9d%91%a2%f0%9d%91%a5-%f0%9d%91%a6-%f0%9d%91%96-%f0%9d%91%a3%f0%9d%91%a5-%f0%9d%91%a6-and-its-complex-conjugate-%f0%9d%91%93%e2%88%97","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-complex-function-%f0%9d%91%93%f0%9d%91%a7-%f0%9d%91%a2%f0%9d%91%a5-%f0%9d%91%a6-%f0%9d%91%96-%f0%9d%91%a3%f0%9d%91%a5-%f0%9d%91%a6-and-its-complex-conjugate-%f0%9d%91%93%e2%88%97\/","title":{"rendered":"A complex function \ud835\udc53(\ud835\udc67) = \ud835\udc62(\ud835\udc65, \ud835\udc66) + \ud835\udc56 \ud835\udc63(\ud835\udc65, \ud835\udc66) and its complex conjugate \ud835\udc53\u2217(\ud835\udc67) = \ud835\udc62(\ud835\udc65, \ud835\udc66) \u2212 \ud835\udc56 \ud835\udc63(\ud835\udc65, \ud835\udc66) are both analytic in the entire complex plane"},"content":{"rendered":"\n<p>Q. A complex function \ud835\udc53(\ud835\udc67) = \ud835\udc62(\ud835\udc65, \ud835\udc66) + \ud835\udc56 \ud835\udc63(\ud835\udc65, \ud835\udc66) and its complex conjugate \ud835\udc53<sup>\u2217<\/sup>(\ud835\udc67) = \ud835\udc62(\ud835\udc65, \ud835\udc66) \u2212 \ud835\udc56 \ud835\udc63(\ud835\udc65, \ud835\udc66) are <em>both <\/em>analytic in the entire complex plane, where \ud835\udc67 = \ud835\udc65 + \ud835\udc56 \ud835\udc66 and \ud835\udc56 = \u221a\u22121 . The function \ud835\udc53 is then given by<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>f(z) = u(x, y) + i v(x, y) <\/p>\n\n\n\n<p>f*(z) = u (x, y) &#8211; i v(x, y) <\/p>\n\n\n\n<p>f(z) is analytic function<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"283\" height=\"249\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-610.png\" alt=\"\" class=\"wp-image-156186\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Q. A complex function \ud835\udc53(\ud835\udc67) = \ud835\udc62(\ud835\udc65, \ud835\udc66) + \ud835\udc56 \ud835\udc63(\ud835\udc65, \ud835\udc66) and its complex conjugate \ud835\udc53\u2217(\ud835\udc67) = \ud835\udc62(\ud835\udc65, \ud835\udc66) \u2212 \ud835\udc56 \ud835\udc63(\ud835\udc65, \ud835\udc66) are both analytic in the entire complex plane, where \ud835\udc67 = \ud835\udc65 + \ud835\udc56 \ud835\udc66 and \ud835\udc56 = \u221a\u22121 . The function \ud835\udc53 is then given by Sol: f(z) = u(x, [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":156187,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5141],"tags":[5140],"offerexpiration":[],"class_list":["post-156183","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156183","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=156183"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156183\/revisions"}],"predecessor-version":[{"id":156188,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156183\/revisions\/156188"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/156187"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=156183"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=156183"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=156183"},{"taxonomy":"offerexpiration","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/offerexpiration?post=156183"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}