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Thanks for this solution! Although the only thing I do not understand is how you go from |1-1/z|/|z-1| to |1/z||z-1|/|z-1|

Question: "The points A, B, C and O represent the numbers z, 1/z, 1 and 0 respectively. Given that 0<argz<pi/2 prove that the angle <OAC = <OCB" Please try this question and see if you can find an elegant proof thank you.