{"id":6509,"date":"2021-10-17T16:36:39","date_gmt":"2021-10-17T11:06:39","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6509"},"modified":"2022-01-16T17:06:22","modified_gmt":"2022-01-16T11:36:22","slug":"addition-of-complex-numbers","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/addition-of-complex-numbers\/","title":{"rendered":"Addition of Complex Numbers – Properties and Examples"},"content":{"rendered":"

Here you will learn subtraction and addition of complex numbers and its properties with examples.<\/p>\n

Let’s begin – <\/p>\n

Addition of Complex Numbers <\/h2>\n

Let \\(z_1\\) = \\(a_1 + ib_1\\) and \\(z_2\\) = \\(a_2 + ib_2\\) be two complex numbers. Then their sum \\(z_1 + z_2\\) is defined as the complex number \\((a_1 + a_2)\\)  + i\\((b_1 + b_2)\\).<\/p>\n

It follows from the definition that the sum \\(z_1 + z_2\\) is a complex number such that<\/p>\n

\n

\\(Re (z_1 + z_2)\\) = \\(Re (z_1)\\) + \\(Re (z_2)\\) and <\/p>\n

\\(Im (z_1 + z_2)\\) = \\(Im (z_1)\\) + \\(Im (z_2)\\)<\/p>\n<\/blockquote>\n

Example<\/span><\/strong> : If \\(z_1\\) = 2 + 3i and \\(z_2\\) = 3 – 2i, then \\(z_1 + z_2\\) = (2 + 3) + (3 – 2)i = 5 + i<\/p>\n

Properties :<\/h3>\n

(i) Addition is Commutative<\/strong> : For any two complex numbers \\(z_1\\) and \\(z_2\\), we have<\/p>\n

\n

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

(ii) Addition is Associative<\/strong> : For any three complex numbers \\(z_1\\), \\(z_2\\), \\(z_3\\), we have<\/p>\n

\n

(\\(z_1\\) + \\(z_2\\)) + \\(z_3\\) =  \\(z_1\\) + (\\(z_2\\) + \\(z_3\\))<\/p>\n<\/blockquote>\n

(iii) Existence of Additive Identity<\/strong> : The complex number 0 = 0 + i0 is the identity element for addition i.e. z + 0 = z = 0 + z for all z \\(\\in\\) C.<\/p>\n

(iv) Existence of Additive Inverse<\/strong> : For any complex number z = a + ib, there exists -z = (-a) + i(-b) such that z + (-z) = 0 = (-z) + z.<\/p>\n

Subtraction of Complex Numbers<\/h2>\n

Let \\(z_1\\) = \\(a_1 + ib_1\\) and \\(z_2\\) = \\(a_2 + ib_2\\) be two complex numbers. Then the subtraction of \\(z_2\\) from \\(z_1\\) is denoted by \\(z_1 – z_2\\) and is defined as the addition of \\(z_1\\) and \\(-z_2\\).<\/p>\n

Example<\/span><\/strong> : If \\(z_1\\) = -2 + 3i and \\(z_2\\) = 4 + 5i, then \\(z_1 – z_2\\) = (-2 + 3i) + (-4 – 5i) = (-2 – 4) + i(3 – 5) = -6 – 2i<\/p>\n\n\n

\n
Next – Multiplication of Complex Numbers \u2013 Properties & Examples<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Complex Number Class 11<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn subtraction and addition of complex numbers and its properties with examples. Let’s begin –  Addition of Complex Numbers  Let \\(z_1\\) = \\(a_1 + ib_1\\) and \\(z_2\\) = \\(a_2 + ib_2\\) be two complex numbers. Then their sum \\(z_1 + z_2\\) is defined as the complex number \\((a_1 + a_2)\\)  + i\\((b_1 …<\/p>\n

Addition of Complex Numbers – Properties and Examples<\/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":[244,229,246,245],"yoast_head":"\nAddition of Complex Numbers - Properties and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn subtraction and addition of complex numbers and its properties 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\/addition-of-complex-numbers\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Addition of Complex Numbers - 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