How to solve $\left|\frac{1 + a + bi}{1 + b - ai}\right| = 1$ I have a problem with solving following equation:
$$\left|\frac{1 + a + bi}{1 + b - ai}\right| = 1$$ (where $a$, $b$ are real numbers and $i$ is an imaginary unit) 
I tried to simplify its left side to something like $c + di$ but I don't know any method to achieve it in this case. Do you have any ideas how do it?

Hint:
Use the fact that for any complex number $z_1$ and $z_2$, $$\left|\frac{z_1}{z_2}\right|=\frac{|z_1|}{|z_2|}$$ Then try and rearrange.
