# Bijective conformal map from half disc to upper half plane

I'm trying to find a bijective conformal map from the half disc $\{z: |z| < 1, \Re(z)>0\}$ to the upper half plane $\{z: \Re(z) > 0\}$. Any help is appreciated. Thanks!

• I don't think you want |z|<0. Maybe |z| < 1 ? – Dylan Yott May 31 '13 at 20:07

Use a Möbius transform to bring one vertex of the half disk to $\infty$ and the other to $0$. Now you have a quadrant. Square to get a half plane.