Unformatted text preview: trigonometric form (sometimes called the polar form ) of the complex number z : For any complex number z = x + yi , we can write z = r (cos θ + i sin θ ) , where (6.3) r =  z  = R x 2 + y 2 and θ = the argument of z . The representation z = r (cos θ + i sin θ ) is often abbreviated as: z = r cis θ (6.4) In the special case z = = + i , the argument θ is unde±ned since r = z  = 0. Also, note that the argument θ can be replaced by θ + 360 ◦ k or θ + π k , depending on whether you are using degrees or radians, respectively, for k = 0, ± 1, ± 2, . .. . Note also that for z = x + yi with r = z  , θ must satisfy tan θ = y x , cos θ = x r , sin θ = y r ....
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 Fall '11
 Dr.Cheun
 Calculus, Complex Numbers, Cos, Complex number, Euler's formula

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