Find the Möbius transformation that applies the domain $$\Omega=\{z\in\mathbb{C}:\Re{z}>0, |z-2|<1\}$$ onto an annulus $$A(0;p,1)\text{ for some }p\in(0,1)$$
I don't even know where to start, I've been told I'm supposed to use $$w=\frac{\zeta-\alpha}{1-\overline{\alpha}\zeta},|\alpha|<1$$ first by defining a function $\zeta=f(z)$ to use the transformation but if I don't know how to start, could someone tell if it's true and give an insight on how to do it?