# Conformal Mapping of Semi-infinite strip

Problem

I'm looking to investigate how the exponential map acts on the semi inifite strip

$$U:=\{z \in \mathbb{C} : Re(z)<0, 0<Im(z)<\pi \}$$

My understanding is that for the infinite strip, the region will be mapped to the UHP, but I'm not sure how the semi infinite condition affects the mapping.

Ultimately I'm looking for a conformal map from $U$ to the UHP.

• $e^{x + i y} = e^x(\cos(y) + i \sin(y))$. – WimC May 27 '12 at 18:10