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If z is a complex number of unit modul...

If z is a complex number of unit modulus and argument q, then `a r g((1+z)/(1+ bar z))` equal

A

`-theta`

B

`pi/2-theta`

C

`theta`

D

`pi-theta`

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `|z|=1` and arg(z)=`theta`
`therefore z=e^(itheta)` and `arg(barz)=e^(-itheta)`
`rArr barz=1/z`
`therefore "arg" (1+z)/(1+barz)="arg"(1+z)/(1+1/z)="arg"(z)=theta`
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