Hey guys, I cant figure this out :

z is a complex number for which

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Can somebody show me how to do this. What I did was to take z = x + iy and then input it into the equation. Rationalised it and then ended up getting x = iy. So z = 2iy. But I still dont get how to solve it? I get that 1+z/1-z has to be totally imaginary for it to have an argument of pi/2.

But with my method it doesnt turn out to be totally imaginary. Its 1+2iy/1-2iy which still has that real component. What am I doing wrong? Am I even on the right track?

Thanks in advance for the help