{"id":4950,"date":"2012-12-12T05:41:46","date_gmt":"2012-12-12T05:41:46","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=4950"},"modified":"2014-12-02T08:27:06","modified_gmt":"2014-12-02T08:27:06","slug":"complex-numbers-continued-amplitude","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/12\/12\/complex-numbers-continued-amplitude\/","title":{"rendered":"Complex Numbers Continued: Amplitude"},"content":{"rendered":"<p>This article assumes you have read our article on <a title=\"Polar Representation of a Complex Number\" href=\"https:\/\/schooltutoring.com\/scholarship\/polar-representation-of-a-complex-number\/\" target=\"_blank\">Polar Representation of a Complex Number<\/a><\/p>\n<p>Resuming from there, we had determined <strong><em>t = tan<sup>-1<\/sup>(b\/a)<\/em><\/strong>, which is called the <strong><em>amplitude or argument of the complex number a+ib and it is denoted by amp(a+ib)<\/em><\/strong>.<\/p>\n<p><strong>Principal amplitude:<\/strong><\/p>\n<p>The value of t which lies in the interval (-\u03c0, \u03c0), is called the principal amplitude of the complex number a+ib. Principal amplitude of a complex number can be found as follows.<\/p>\n<p>First find t = tan<sup>-1<\/sup>|b\/a|<\/p>\n<p>Then the principal amplitude is,<\/p>\n<p>a)\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><em>t<\/em><\/strong>, if both <strong><em>a<\/em><\/strong> and <strong><em>b<\/em><\/strong> are positive<\/p>\n<p>b)\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><em>\u03c0-t<\/em><\/strong>, if <strong><em>a<\/em><\/strong> is negative and <strong><em>b<\/em><\/strong>\u00a0 is positive<\/p>\n<p>c)\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><em>\u2013( \u03c0-t), <\/em><\/strong>if both <strong><em>a<\/em><\/strong> and <strong><em>b<\/em><\/strong> are negative<\/p>\n<p>d)\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><em>\u2013t<\/em><\/strong>, if <strong><em>a <\/em><\/strong>is positive and <strong><em>b<\/em><\/strong> is negative<\/p>\n<p><strong>Properties of amplitude:<\/strong><\/p>\n<p>For any two complex numbers Z<sub>1<\/sub> and Z<sub>2<\/sub>,<\/p>\n<p>(i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Amp(Z<sub>1<\/sub> Z<sub>2<\/sub>) = Amp (Z<sub>1<\/sub>) + Amp (Z<sub>2<\/sub>)<\/p>\n<p>(ii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Amp(Z<sub>1<\/sub> \/Z<sub>2<\/sub>) = Amp (Z<sub>1<\/sub>) &#8211; Amp (Z<sub>2<\/sub>)<\/p>\n<p>We also offer English tutoring, <a href=\"https:\/\/schooltutoring.com\/english-tutors\/\">click here<\/a> for more information.<\/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 Jamestown visit: <a href=\"https:\/\/schooltutoring.com\/tutoring-in-jamestown-north-dakota\/\">Tutoring in Jamestown, ND. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This article assumes you have read our article on Polar Representation of a Complex Number Resuming from there, we had determined t = tan-1(b\/a), which is called the amplitude or argument of the complex number a+ib and it is denoted by amp(a+ib). Principal amplitude: The value of t which lies in the interval (-\u03c0, \u03c0), [&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],"tags":[91,1137,1184,1363,1388,1412],"class_list":["post-4950","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-amplitude","tag-modulus","tag-negative","tag-positive","tag-principal","tag-properties"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/4950","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=4950"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/4950\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=4950"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=4950"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=4950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}