{"id":2545,"date":"2012-07-18T22:46:31","date_gmt":"2012-07-18T22:46:31","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=2545"},"modified":"2014-12-02T08:32:08","modified_gmt":"2014-12-02T08:32:08","slug":"modulus-and-conjugate-of-a-complex-number","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/07\/18\/modulus-and-conjugate-of-a-complex-number\/","title":{"rendered":"Modulus and Conjugate of a Complex Number"},"content":{"rendered":"<p>Their are two important data points to calculate, based on <a href=\"https:\/\/schooltutoring.com\/tutoring-programs\/math-tutoring\/\">complex numbers<\/a>. They are the Modulus and Conjugate.<\/p>\n<h4>Modulus of a complex number:<\/h4>\n<p>The modulus of a complex number z=a+ib is denoted by |z| and is defined as <a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/modulus-and-conjugate-of-complex-number1.bmp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-2546\" title=\"modulus and conjugate of complex number1\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/modulus-and-conjugate-of-complex-number1.bmp\" alt=\"\" \/><\/a>.<\/p>\n<p><strong><span style=\"text-decoration: underline\">Example:<\/span><\/strong><\/p>\n<p>Find the modulus of z =4 \u2013 3i.<\/p>\n<p><strong><span style=\"text-decoration: underline\">Solution:<\/span><\/strong><\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/modulus-and-conjugate-of-complex-number2.bmp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-2547\" title=\"modulus and conjugate of complex number2\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/modulus-and-conjugate-of-complex-number2.bmp\" alt=\"\" \/><\/a><\/p>\n<h5>Properties of conjugate:<\/h5>\n<p>(i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 |z|=0 \u00a0z=0<\/p>\n<p>(ii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 |-z|=|z|<\/p>\n<p>(iii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 |z1 * z2|= |z1| * |z2|<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/modulus-and-conjugate-of-complex-number3.bmp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-2548\" title=\"modulus and conjugate of complex number3\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/modulus-and-conjugate-of-complex-number3.bmp\" alt=\"\" \/><\/a><\/p>\n<h4>Conjugate of a complex number:<\/h4>\n<p>The conjugate of a complex number z=a+ib is denoted by <a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/modulus-and-conjugate-of-complex-number4.bmp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-2549\" title=\"modulus and conjugate of complex number4\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/modulus-and-conjugate-of-complex-number4.bmp\" alt=\"\" \/><\/a>and is defined as <strong><\/strong><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/modulus-and-conjugate-of-complex-number5.bmp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-2550\" title=\"modulus and conjugate of complex number5\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/modulus-and-conjugate-of-complex-number5.bmp\" alt=\"\" \/><\/a>.<\/p>\n<h5>Properties of conjugate:<\/h5>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/modulus-and-conjugate-of-complex-number6.bmp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-2551\" title=\"modulus and conjugate of complex number6\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/modulus-and-conjugate-of-complex-number6.bmp\" alt=\"\" \/><\/a><\/p>\n<p><span class=\"tutorOrange\">SchoolTutoring Academy<\/span> 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. To learn more about how we help parents and students in Orange visit: <a href=\"https:\/\/schooltutoring.com\/tutoring-in-orange-california\/\">Tutoring in Orange. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Their are two important data points to calculate, based on complex numbers. They are the Modulus and Conjugate. Modulus of a complex number: The modulus of a complex number z=a+ib is denoted by |z| and is defined as . Example: Find the modulus of z =4 \u2013 3i. Solution: Properties of conjugate: (i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 |z|=0 \u00a0z=0 [&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":[2,11],"tags":[341,384,1137,1138,1412],"class_list":["post-2545","post","type-post","status-publish","format-standard","hentry","category-algebra","category-math-fundamentals","tag-complex","tag-conjugateofcomplexnumbers","tag-modulus","tag-modulus-of-complex-numbers","tag-properties"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2545","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=2545"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2545\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=2545"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=2545"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=2545"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}