{"id":822,"date":"2012-02-23T16:56:23","date_gmt":"2012-02-23T16:56:23","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=822"},"modified":"2014-12-02T08:33:48","modified_gmt":"2014-12-02T08:33:48","slug":"multiply-and-divide-complex-numbers","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/02\/23\/multiply-and-divide-complex-numbers\/","title":{"rendered":"Multiply and Divide Complex Numbers"},"content":{"rendered":"<p><strong>Multiplication of Complex Numbers<\/strong><\/p>\n<p>The product of complex numbers a + b<em>i<\/em> and c + d<em>i<\/em> is given as:<\/p>\n<p>(a + b<em>i<\/em>) + (c + d<em>i<\/em>) = (ac \u2013 bd) + (ad + bc)<em>i<\/em><\/p>\n<p>Example:<\/p>\n<p>(4 \u2013 2<em>i<\/em>)(3 + 5<em>i<\/em>) = 4(3 + 5<em>i<\/em>) \u2013 2<em>i<\/em>(3 + 5<em>i<\/em>)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (Using distributive property over addition)<\/p>\n<p>= 12 + 20<em>i<\/em> \u2013 6<em>i <\/em>\u2013 10<em>i<\/em><sup>2<\/sup> = 12 + 20<em>i<\/em> \u2013 6<em>i <\/em>+ 10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (As <em>i<\/em><sup>2<\/sup> = -1)<\/p>\n<p>= 22 + 14<em>i\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em>\u00a0\u00a0\u00a0 (Grouping like terms)<em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em><\/p>\n<p><strong>Division of Complex Numbers<em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em><\/strong><\/p>\n<p>Multiply both numerator and denominator by conjugate of denominator and simplify<\/p>\n<p>Example:<\/p>\n<p><a href=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/div-com-num.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-823\" src=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/div-com-num.png\" alt=\"\" width=\"159\" height=\"186\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Multiplication of Complex Numbers The product of complex numbers a + bi and c + di is given as: (a + bi) + (c + di) = (ac \u2013 bd) + (ad + bc)i Example: (4 \u2013 2i)(3 + 5i) = 4(3 + 5i) \u2013 2i(3 + 5i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (Using distributive property over addition) = 12 [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2,13],"tags":[525,1166,1250],"class_list":["post-822","post","type-post","status-publish","format-standard","hentry","category-algebra","category-pre-algebra","tag-diviidecomplexnumbers","tag-multiplycomplexnumebrs","tag-operationsoncomplexnumbersadditionofcomplexnumbers"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/822","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=822"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/822\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=822"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=822"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=822"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}