$\displaystyle \mid z \mid = 1$

$\displaystyle \mid a \mid < -1$

$\displaystyle \left|\frac{z-a}{1-\overline{a}z}\right|$

i tried:

$\displaystyle z = x + yi$

$\displaystyle a = a + bi$

$\displaystyle \left|\frac{z-a}{1-\overline{a}z}\right| =$

$\displaystyle = \left|\frac{x + yi - i(a + bi)}{1- (a - bi) (x + yi)}\right|$

and got nothing useful.. is there any other way? how do you solve this?