If `|z|=1` and `w=(z-1)/(z+1)` (where `z!=-1),` then `R e(w)` is 0 (b) `1/(|z+1|^2)` `|1/(z+1)|,1/(|z+1|^2)` (d) `(sqrt(2))/(|z|1""|^2)`

Options

A. 0
B. `-1/(|z+1|^(2))`
C. `|z/(z+1)|.1/(|z+1|^(2))`
D. `sqrt(2)/|z+1|^(2)`

Answer

A

Explanation

We have, `|z|=1`,So, let `z=costheta+sintheta`. Then,
`omega=(z-1)/(z+1) = (costheta+isintheta-1)/(costheta+isintheta+1) = 2itantheta//2 rArr "Re"(omega)=0`