If `|z|=1a n dz!=+-1,` then all the values of `z/(1-z^2)` lie on a line not passing through the origin `|z|=sqrt(2)` the x-axis (d) the y-axis

Options

A. a line not passing through the origin
B. `|z|=sqrt(2)`
C. the x-axis
D. the y-axis

Answer

D

Explanation

We have,
`|z|=1 rArr z=costheta+isintheta`
Let `omega=z/(1-z^(2))`. Then,
`omega=(costheta+isintheta)/(1-(cos2theta+isin2theta))`
`rArr omega=(costheta+isintheta)/(2sin^(2)theta-2isinthetacostheta)=-1/(2isintheta)=1/(2sintheta)i`
`rArr omega` lies on the y-axis.