{"id":2538,"date":"2012-07-19T20:14:52","date_gmt":"2012-07-19T20:14:52","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=2538"},"modified":"2014-12-02T08:32:08","modified_gmt":"2014-12-02T08:32:08","slug":"operations-on-complex-numbers","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/07\/19\/operations-on-complex-numbers\/","title":{"rendered":"Operations on Complex Numbers"},"content":{"rendered":"

A number which is of the form a+ib<\/strong>, where a<\/strong> and b<\/strong> are real numbers and i2<\/sup> =-1<\/strong>, is called a complex number and is usually denoted by z<\/strong>.<\/p>\n

i.e. z=a+ib<\/strong>.<\/p>\n

Here \u2018a<\/strong>\u2019 is called the real part of z<\/strong> , i.e. Re<\/strong>(z<\/strong>) = a<\/strong><\/p>\n

And \u2018b<\/strong>\u2019 is called the imaginary part of z, i.e. Im<\/strong>(z<\/strong>)=b<\/strong>.<\/p>\n

Sum of complex numbers:<\/h4>\n

If z1 = a+ib<\/strong> and z2 = c+id<\/strong> then the sum of z1<\/strong> and z2<\/strong> is denoted by z1+z2<\/strong> and is defined as<\/p>\n

Z1+z2 = (a+c)+i(b+d).<\/strong><\/p>\n

Example:<\/span><\/strong><\/p>\n

Find the sum of z1 = 3+5i<\/strong> and z2 = 4-2i.<\/strong><\/p>\n

Solution:<\/span><\/strong><\/p>\n

By the definition of sum of complex numbers,<\/p>\n

Z1+z2 = (3+4) + i(5-2) = 7 + 3i.<\/strong><\/p>\n

Difference of complex numbers:<\/h4>\n

If z1 = a+ib<\/strong> and z2 = c+id<\/strong> then the difference of z1<\/strong> and z2<\/strong> is denoted by z1-z2<\/strong> and is defined as<\/p>\n

Z1-z2 = (a-c)+i(b-d).<\/strong><\/p>\n

Example:<\/span><\/strong><\/p>\n

If\u00a0 z1 = 3+5i<\/strong> and z2 = 4-2i<\/strong> find z1-z2.<\/strong><\/p>\n

Solution:<\/span><\/strong><\/p>\n

By the definition of difference of complex numbers,<\/p>\n

z1-z2 = (3-4) + i(5+2) = -1 + 7i.<\/strong><\/p>\n

Product of complex numbers:<\/h4>\n

If z1 = a+ib<\/strong> and z2 = c+id<\/strong> then the product of z1<\/strong> and z2<\/strong> is denoted by z1.z2<\/strong> and is defined as,<\/p>\n

z1.z2 = (ac-bd) + i(bc + ad).<\/strong><\/p>\n

Example:<\/span><\/strong><\/p>\n

Find the product of z1 = 3+5i<\/strong> and z2 = 4-2i.<\/strong><\/p>\n

Solution:<\/span><\/strong><\/p>\n

By the definition of product of complex numbers,<\/p>\n

z1.z2 = (12+10)+i(20-6) = 22 + 14i<\/strong><\/p>\n

Division of complex numbers:<\/h4>\n

If z1 = a+ib<\/strong> and z2 = c+id<\/strong> then the quotient of z1<\/strong> and z2<\/strong> is denoted by z1\/z2<\/strong> and is defined as,<\/p>\n

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

Example:<\/span><\/strong><\/p>\n

If\u00a0 z1 = 3+5i<\/strong> and z2 = 4-2i <\/strong>find z1\/z2.<\/strong><\/p>\n

Solution:<\/span><\/strong><\/p>\n

By the definition of division of complex numbers,<\/p>\n

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

 <\/p>\n

 <\/p>\n

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

A number which is of the form a+ib, where a and b are real numbers and i2 =-1, is called a complex number and is usually denoted by z. i.e. z=a+ib. Here \u2018a\u2019 is called the real part of z , i.e. Re(z) = a And \u2018b\u2019 is called the imaginary part of z, i.e. […]<\/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":[342,494,529,1244,1396,1774],"class_list":["post-2538","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-complex-number","tag-difference","tag-division","tag-oparations","tag-product","tag-sum"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2538","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=2538"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2538\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=2538"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=2538"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=2538"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}