Complex question

From: JamesLan (jlan1234_at_hotmail-dot-com.no-spam.invalid)
Date: 03/29/05 

Date: 29 Mar 2005 17:36:46 -0600

Hi I have this question that I am having a little problem with

Find complex numbers z that satisfy simultaneously:

z*(z-conjugate) = |12 + 5i| - |4 - 3i| and Re((1 - i)z) = 3

I think I can do the second part as
(1-i)z = (1-i)*(x+iy) = x - xi + iy + y

So Re((1-i)z) = x + y = 3

Im having a little trouble with the first part
z*(z-conjugate) = |12 + 5i| - |4 - 3i|

I am doing this:
(x + iy)*(x - iy) = root(12^2 + 5^2) - root(4^2 + 3^2)
x^2 + y^2 = 13 - 5
x^2 + y^2 = 8

This gives me two simultaneous equations that I can solve that would
give 2 solutions for z, I was just wondering if this is what is
supposed to be done to solve the problem or am I doing it wrong?

Thanks
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