1. ## Complex number

/z/=1 and w=(z-1)/(z+1) [where z not equal to -1], then find Re(w).

2. Originally Posted by matsci0000
/z/=1 and w=(z-1)/(z+1) [where z not equal to -1], then find Re(w).
Here is a hint: $w = \frac{{z - 1}}{{z + 1}} = \frac{{z\overline z + z + \overline z - 1}}{{\left| {z + 1} \right|^2 }}$

3. Hi

|z| being equal to 1, you can let $|z| = e^{i\theta}$

Then $\frac{z-1}{z+1} = \frac{e^{i\theta}-1}{e^{i\theta}+1}$

$\frac{z-1}{z+1} = \frac{e^{i\frac{\theta}{2}}(e^{i\frac{\theta}{2}}-e^{-i\frac{\theta}{2}})}{e^{i\frac{\theta}{2}}(e^{i\fr ac{\theta}{2}}+e^{-i\frac{\theta}{2}})}$

Can you go on now ?

EDIT : too late ...