Question

Find the locus of z/(1-z^2), where z lies on the circle of radius 1 centered at origin and z≠±1.

(a) line not passing through origin

(b) |z|=√2

(c) real axis

(d) imaginary axis

I had been asked this question by my college director while I was bunking the class.

This key question is from Regions in the Complex Plane in section Complex Numbers of Engineering Mathematics

Answer 1

The correct choice is (d) imaginary axis

For explanation I would say: Given |z|=1 and z≠±1, write ω=z/(1-z^2)=z/(zz̅-z^2)=1/(z̅-z).

Hence ω is a purely imaginary number and lies on imaginary axis.