{"id":6507,"date":"2021-10-17T16:00:08","date_gmt":"2021-10-17T10:30:08","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6507"},"modified":"2021-11-21T18:27:46","modified_gmt":"2021-11-21T12:57:46","slug":"complex-number-class-11","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/complex-number-class-11\/","title":{"rendered":"Complex Number Class 11"},"content":{"rendered":"

Here you will learn what is the complex number class 11 and equality of complex numbers with examples.<\/p>\n

Let’s begin – <\/p>\n

Complex Number Class 11<\/h2>\n

If a, b are two real numbers, then a number of the form a + ib is called aa complex number.<\/p>\n

Example<\/strong><\/span> : 7 + 2i, -1 + i, 3 – 2i, 0 + 2i, 1 + 0i etc. are complex numbers<\/p>\n

Real and imaginary parts of a complex number<\/strong> : If z = a + ib is a complex number, then ‘a’ is called the real part of z and ‘b’ is known as the imaginary part of z.<\/p>\n

The real part of z is denoted Re (z) and the imaginary part by Im (z).<\/p>\n

Example<\/span><\/strong> : If z = 3 – 4i, then Re (z) = 3 and Im (z) = -4.<\/p>\n

Purely real and purely imaginary complex numbers<\/strong> : A complex number z is purely real if its imaginary part is zero i.e. Im (z) = 0 and purely imaginary if its real part is zero i.e. Re (z) = 0.<\/p>\n

Set of Complex Numbers<\/strong> : The set of all complex numbers is denoted by C i.e. C = {a + ib : a, b \\(\\in\\) R}.<\/p>\n

Since a real number ‘a’ can be written as a + 0i. Therefore, every real number is a complex number number. Hence, R \\(\\subset\\) C, where R is the set of all real numbers.<\/p>\n

Equality of Complex Numbers<\/h2>\n

Two Complex numbers \\(z_1\\) = \\(a_1 + ib_1\\) and \\(z_2\\) = \\(a_2 + ib_2\\)  are equal if<\/p>\n

\n

\\(a_1\\) = \\(a_2\\) and \\(b_1\\) = \\(b_2\\)<\/p>\n

i.e. \\(Re(z_1)\\) = \\(Re(z_2)\\) and \\(Im(z_1)\\) = \\(Im(z_2)\\)<\/p>\n<\/blockquote>\n

Example<\/span><\/strong> : If \\(z_1\\) = 2 – iy and \\(z_2\\) = x + 3i are equal, find x and y.<\/p>\n

Solution<\/span><\/strong> : We have, <\/p>\n

\\(z_1\\) = \\(z_2\\)<\/p>\n

\\(\\implies\\) 2 – iy = x + 3i \\(\\implies\\) 2 = x and -y = 3 \\(\\implies\\) x = 2 and y = -3<\/p>\n\n\n

\n
Next – Addition of Complex Numbers \u2013 Properties & Example<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Integral Powers of Iota<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the complex number class 11 and equality of complex numbers with examples. Let’s begin –  Complex Number Class 11 If a, b are two real numbers, then a number of the form a + ib is called aa complex number. Example : 7 + 2i, -1 + i, 3 …<\/p>\n

Complex Number Class 11<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[41],"tags":[247,229],"yoast_head":"\nComplex Number Class 11 - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the complex number class 11 and equality of complex numbers with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/complex-number-class-11\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Complex Number Class 11 - 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