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I need to find one solution to the follow set of complex equations:

a*a+b*b = 1-K-K/2

a*b+c*d=K/2

c*c+d*d=1-K/2

where K is some real constant.

This is equivalent to finding a 2x2 complex matric M such that [tex]M^\dagger M=[/tex]

1-K-K/2, -K/2

-K/2, 1-K/2

I can't seem to do get started.