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If |z|=1 and z'=(1+z^(2))/(z), then...

If `|z|=1` and `z'=(1+z^(2))/(z)`, then

A

`z'` lie on a line not passing through origin

B

`|z'|=sqrt(2)`

C

`Re(z')=0`

D

`Im(z')=0`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `z'=(1+z^(2))/(z)=(zbarz+z)/(z)=z+barz` which is purely real.
`implies Im(z')=0`
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