Complex variables, maximum value

[babyrudin]

Homework Equations

Let $$w \in C$$ be a fixed complex number with $$|w|<1$$. Let
$$f(z)=\frac{z-w}{1-\bar{w}z}.$$
Calculate its maximum value in the region $$|z| \leq 1$$.

The Attempt at a Solution

How should I approach this? Not sure if maximum modulus principle is of much help.

 

[babyrudin]

Any idea on this?