How can I transform by a conformal mapping the annulus $\{w \in \mathbb{C} : 1<|w|<2\}$ to $\{z \in \mathbb{C}: R(z)>0, |z-h|>1\}$.
I noticed that I need some Möbius transform that turn one disc in another disc (with center $h$) and one disc in a line, so it must be of the form $1/z-a$ where $a$ is some point of the boundary of the circumference but I can't force those conditions to give that specific disc in the image.