complex l-8

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Complex functions A function of a complex variable is a mapping f which associate eac h complex number z = x + i y to another complex number w = u + i v. W e write: w = f ( z), u + i v = f ( x + i y). w is also called Image of z and z is called Pre-image. EXAMPLES If w = z 2 , then u = x 2 - y 2 , v = 2 xy. If w = 1/ z, where z is not 0, t hen u = x/( x 2 + y 2 ), v = - y/ ( x 2 + y 2 ). If w = z*, then u = x, v = -y. If w = | z | , then 2 2 , 0. u x y v ! !

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