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Math Help - zeros of a polynomial with complex coefficients

  1. #1
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    zeros of a polynomial with complex coefficients

    How do I find the roots of this polynomial with complex coefficients:

    p(z) = z2-(1+2i)z + (- (3/2)+2i)

    Is there a general method?
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  2. #2
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    Re: zeros of a polynomial with complex coefficients

    yes - the quadratic equation.
    Square roots of complex numbers are generally calculated by putting them into polar form first:

    x + iy = \sqrt{x^2 + y^2}e^{i\tan^{-1}(y/x)} when x>0,

    x + iy = \sqrt{x^2 + y^2}e^{i(\pi + \tan^{-1}(y/x))} when x<0,

    x + iy = \sqrt{x^2 + y^2}e^{i \pi/2 } when x=0, y>0,

    x + iy = \sqrt{x^2 + y^2}e^{- i \pi/2 } when x=0, y<0.
    Last edited by johnsomeone; September 29th 2012 at 02:46 PM.
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