{"id":3175,"date":"2024-08-26T22:32:52","date_gmt":"2024-08-26T22:32:52","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=3175"},"modified":"2024-08-26T22:32:53","modified_gmt":"2024-08-26T22:32:53","slug":"the-polar-form-of-a-complex-number","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/26\/the-polar-form-of-a-complex-number\/","title":{"rendered":"The Polar Form of a Complex Number"},"content":{"rendered":"\n
\"image\"\/<\/figure>\n\n\n\n

Figure 7.3<\/strong> Polar form of complex numbers<\/p>\n\n\n\n

This latter form is usually abbreviated to Z<\/strong><\/em>=r<\/strong><\/em>\u2220\u03b8<\/strong>, and is called the polar form of a complex number.<\/p>\n\n\n\n

r<\/em> is called the modulus<\/em> (or magnitude of Z<\/em>) and is written as mod Z<\/em> or |Z<\/em>|. r<\/em> is determined from Pythagoras\u2019s theorem on triangle OAZ:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

The modulus is represented on the Argand diagram by the distance OZ. \u03b8 is called the argument (or amplitude) of Z<\/em> and is written as arg Z<\/em>. \u03b8 is also deduced from triangle OAZ<\/em>: arg Z<\/em>=\u03b8=tan-1<\/sup>y<\/em>\/x<\/em>.<\/p>\n\n\n\n

For example, the cartesian complex number (3+j<\/strong><\/em>4) is equal to r<\/em>\u2220\u03b8 in polar form, where \"image\" and,<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Hence, \"image\"<\/p>\n\n\n\n

Similarly, (\u20133+j<\/em>4) is shown in\u00a0Figure 7.3(b),<\/p>\n\n\n\n

where, \"image\"<\/p>\n\n\n\n

and, \"image\"<\/p>\n\n\n\n

Hence, (\u20133<\/strong>+j<\/strong><\/em>4<\/strong>)=5\u2220126.87<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Figure 7.3 Polar form of complex numbers This latter form is usually abbreviated to Z=r\u2220\u03b8, and is called the polar form of a complex number. r is called the modulus (or magnitude of Z) and is written as mod Z or |Z|. r is determined from Pythagoras\u2019s theorem on triangle OAZ: The modulus is represented on the Argand diagram by the distance OZ. \u03b8 is […]<\/p>\n","protected":false},"author":1,"featured_media":3168,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[428],"tags":[],"class_list":["post-3175","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-complex-numbers"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/mathematics.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3175","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=3175"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3175\/revisions"}],"predecessor-version":[{"id":3176,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3175\/revisions\/3176"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/3168"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=3175"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=3175"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=3175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}