# Thread: find a complex number given modulus of another

1. ## find a complex number given modulus of another

If z = x + iy, and the modulus of z is 1, then find:
$\frac{z - 1}{z + 1}$

2. Originally Posted by differentiate
If z = x + iy, and the modulus of z is 1, then find:
$\frac{z - 1}{z + 1}$
Well, what have you tried?

To start you off you could try:

$
\frac{z - 1}{z + 1}=\frac{(x-1)+iy}{(x+1)+iy}
$

CB

3. Multiply both numerator and denominator by $\overline{z}+ 1$.
A miracle occurs!