{"id":156459,"date":"2023-08-31T12:17:24","date_gmt":"2023-08-31T06:47:24","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=156459"},"modified":"2023-08-31T12:17:34","modified_gmt":"2023-08-31T06:47:34","slug":"a-harmonic-function-is-analytic-if-it-satisfies-the-laplace-equation-if-%f0%9d%91%a2%f0%9d%91%a5-%f0%9d%91%a6-2%f0%9d%91%a52-%e2%88%92-2%f0%9d%91%a62-4%f0%9d%91%a5%f0%9d%91%a6-is-a-harmonic","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-harmonic-function-is-analytic-if-it-satisfies-the-laplace-equation-if-%f0%9d%91%a2%f0%9d%91%a5-%f0%9d%91%a6-2%f0%9d%91%a52-%e2%88%92-2%f0%9d%91%a62-4%f0%9d%91%a5%f0%9d%91%a6-is-a-harmonic\/","title":{"rendered":"A harmonic function is analytic if it satisfies the Laplace equation. If \ud835\udc62(\ud835\udc65, \ud835\udc66) = 2\ud835\udc652 \u2212 2\ud835\udc662 + 4\ud835\udc65\ud835\udc66 is a harmonic"},"content":{"rendered":"\n

Q. A harmonic function is analytic if it satisfies the Laplace equation. If \ud835\udc62(\ud835\udc65, \ud835\udc66) = 2\ud835\udc652<\/sup> \u2212 2\ud835\udc662<\/sup> + 4\ud835\udc65\ud835\udc66 is a harmonic function, then its conjugate harmonic function \ud835\udc63(\ud835\udc65, \ud835\udc66) is<\/p>\n\n\n\n

             (A) 4\ud835\udc65\ud835\udc66 \u2212 2\ud835\udc652<\/sup> + 2\ud835\udc662<\/sup> + constant<\/p>\n\n\n\n

             (B) 4\ud835\udc662<\/sup> \u2212 4\ud835\udc65\ud835\udc66 + constant<\/p>\n\n\n\n

             (C) 2\ud835\udc652<\/sup> \u2212 2\ud835\udc662<\/sup> + \ud835\udc65\ud835\udc66 + constant<\/p>\n\n\n\n

             (D) \u22124\ud835\udc65\ud835\udc66 + 2\ud835\udc662<\/sup> \u2212 2\ud835\udc652<\/sup> + constant<\/p>\n\n\n\n

Ans: 4xy \u2212 2x2<\/sup> + 2y2<\/sup> + constant<\/p>\n\n\n\n

Sol:<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Q. A harmonic function is analytic if it satisfies the Laplace equation. If \ud835\udc62(\ud835\udc65, \ud835\udc66) = 2\ud835\udc652 \u2212 2\ud835\udc662 + 4\ud835\udc65\ud835\udc66 is a harmonic function, then its conjugate harmonic function \ud835\udc63(\ud835\udc65, \ud835\udc66) is              (A) 4\ud835\udc65\ud835\udc66 \u2212 2\ud835\udc652 + 2\ud835\udc662 + constant              (B) 4\ud835\udc662 \u2212 4\ud835\udc65\ud835\udc66 + constant              (C) 2\ud835\udc652 \u2212 2\ud835\udc662 + […]<\/p>\n","protected":false},"author":419,"featured_media":156461,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-156459","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\/156459","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=156459"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156459\/revisions"}],"predecessor-version":[{"id":156462,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156459\/revisions\/156462"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/156461"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=156459"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=156459"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=156459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}