The question is to
Find a conformal map from $D$ onto $D\setminus \left[\frac{-1}{2},1\right)$.
I don't know how to start with. The line $\left[\frac{-1}{2},1\right)$ makes it crazy. Anyone can give me some hints?
The question is to
Find a conformal map from $D$ onto $D\setminus \left[\frac{-1}{2},1\right)$.
I don't know how to start with. The line $\left[\frac{-1}{2},1\right)$ makes it crazy. Anyone can give me some hints?
First map $D$ onto itself with a Möbius. $ L(z)=\frac{ z-\alpha}{ 1 -\bar{\alpha} z}$ where $\alpha=-\frac{1}{2}$. Then follow with $z \to -z$ and finally with $\sqrt{z}$. That will give you the intersection of $D$ with the right half plane. From there it is easy.