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You would solve it like any other equation...isolate z. Then you manipulate the expression to get it into the form of a+jb. One trick is that since j*j = -1, you can multiply expressions like (x+jy) by it's conjugate divided by it's conjugateTHis means you would multiply the expression by (x-jy) / (x-jy) = 1. Since it's equal to one, you aren't changing the expression. YOu are just changing the way it looks.
(x+jy)*(x-jy)/(x-jy) = (x^2+y^2)/(x-jy).
What this lets you do is move the complex j expression between the numerator and denominator. ANd if you do it right, it probably divides itself out, or puts the j in a place where you want it.