Math Help - zeros of a polynomial with complex coefficients

1. 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?

2. Re: zeros of a polynomial with complex coefficients

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 $x=0, y<0$.