I need to find a conformal map $$f\colon \mathbb{D} \to \{z\;|\;|z|<1,\,z\notin \mathbb{R}_{\geq 0}\}.$$ This is an excercise from one of my books and their solution is completely different from mine. I don't even know if mine is correct so I wanted to ask you. I uploaded a picture where you can see what I tried.
$\mathbb{D}$ is the open unit disk.
In my case a conformal map is biholomorphic(bijective and holomorphic with holomorphic inverse).
