{"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
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 Two Complex numbers \\(z_1\\) = \\(a_1 + ib_1\\) and \\(z_2\\) = \\(a_2 + ib_2\\) are equal if<\/p>\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\nEquality of Complex Numbers<\/h2>\n
\n