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Find the where the complex number z/1-z^2 lies on

Source: MTRP 2016 Class 11-Multiple Choice Question: Problem 3 :-

May 31, 2020
complex numbers

Problem Statement

zz is a complex number and ∣z∣=1|z|=1 and z2≠1z^2\neq 1. Then z1−z2\frac{z}{1-z^2} lies on
[*] A line not passing through origin [*] ∣z∣=2|z|=2 [*] xx-axis [*] yy-axis
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