/z/=1 and w=(z-1)/(z+1) [where z not equal to -1], then find Re(w).
Hi
|z| being equal to 1, you can let $\displaystyle |z| = e^{i\theta}$
Then $\displaystyle \frac{z-1}{z+1} = \frac{e^{i\theta}-1}{e^{i\theta}+1}$
$\displaystyle \frac{z-1}{z+1} = \frac{e^{i\frac{\theta}{2}}(e^{i\frac{\theta}{2}}-e^{-i\frac{\theta}{2}})}{e^{i\frac{\theta}{2}}(e^{i\fr ac{\theta}{2}}+e^{-i\frac{\theta}{2}})}$
Can you go on now ?
EDIT : too late ...