(a) Find the Mobius's transformation $f(z)$ mapping the unit disk $\{z\colon |z|<1\}$ onto exterior $\{w\colon |w|>1\}$ of the unit disk, such that $f(0)=5$ and $f(-1)=-1$.
(b) Find the fixed points of $f$ (points s.t. $f(z)=z$).
(c) Find the stretch ($|f'(z)|$) and the rotation angle ($\arg(f'(z))$) of $f$ at $z$.
