{"id":4828,"date":"2012-11-07T03:46:05","date_gmt":"2012-11-07T03:46:05","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=4828"},"modified":"2014-12-02T08:31:57","modified_gmt":"2014-12-02T08:31:57","slug":"operations-on-polar-form-of-a-complex-number","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/11\/07\/operations-on-polar-form-of-a-complex-number\/","title":{"rendered":"Operations on Polar Form of a Complex Number"},"content":{"rendered":"

The polar form of a complex number a+ib is a+ib = r(Cos t + i Sin t), where r is its modulus and t is its argument. As we operate on the real numbers, we can perform operations on complex numbers also. The operations on the complex numbers are as follows.<\/p>\n

Equal numbers in polar form:<\/h5>\n

If two complex numbers are same then their modulus are same and their arguments differ by 2k\u03c0.<\/p>\n

If r(Cos t + i Sint) = R (Cos T + i Sin T)<\/p>\n

Then r = R and t = 2k\u03c0 + T.<\/p>\n

Conjugate of a complex number in polar form:<\/h5>\n

As we know, the conjugate of the complex number a+ib is a-ib. So, the conjugate of a complex number in r(Cos t + i Sint) is r(Cos (-t) + i Sin(-t)).<\/p>\n

Inverse of a complex number in polar form:<\/h5>\n

We have,<\/p>\n

\"\"<\/a><\/p>\n

So, for inverting a complex number in polar form, we just need to invert its modulus and change the sign of its argument.<\/p>\n

Product in polar form:<\/h5>\n

We have,<\/p>\n

r(Cos t + i Sint) * R (Cos T + i Sin T)<\/p>\n

= rR (Cost Cos T- Sin t Sin T) + i rR (Sint CosT + Cos t Sin T)<\/p>\n

= rR [Cos(t+T) + i Sin (t+T)]\n

So, for multiplying two complex numbers in polar form, we just need to multiply the moduli and add the arguments.<\/p>\n

Quotient in polar form:<\/h5>\n

We have,<\/p>\n

\"\"<\/a><\/p>\n

So, for dividing the complex numbers in polar form, we just need to divide their moduli and subtract their arguments in order.<\/p>\n

Do you need more help with Mathematics? Take a look at our Mathematics tutoring services.<\/a><\/p>\n

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 British-Columbia visit: Tutoring in British-Columbia.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

The polar form of a complex number a+ib is a+ib = r(Cos t + i Sin t), where r is its modulus and t is its argument. As we operate on the real numbers, we can perform operations on complex numbers also. The operations on the complex numbers are as follows. Equal numbers in polar […]<\/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":[383,586,969,1396,1467],"class_list":["post-4828","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-conjugate","tag-equal-numbers","tag-inverse","tag-product","tag-quotient"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/4828","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=4828"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/4828\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=4828"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=4828"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=4828"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}