Find the locus of z/(1-z2), where z lies on the circle of radius 1 centered at origin and z≠±1.

Find the locus of z/(1-z2), where z lies on the circle of radius 1 centered at origin and z≠±1. Correct Answer imaginary axis

Given |z|=1 and z≠±1, write ω=z/(1-z2)=z/(zz̅-z2)=1/(z̅-z). Hence ω is a purely imaginary number and lies on imaginary axis.

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