Hey /sci i was wondering if someone could please help with this problem, i've tried and tried and just keep getting nowhere.

If the locus of Z is semi circle with radius 1, so that Im (z) is greater than or equal to 0, and W is defined in the picture, find the corresponding locus of w and sketch it on a diagram.

I've tried to make w real by multiplying by the complex conjugate, i have no idea if this is even the right way to solve it thought/ if it is, what to do next.