# 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.

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It maps to the uppar half of the unit disc. –  WimC May 27 '12 at 18:05
@WimC: Thanks, are you able to briefly explain why? –  Mathmo May 27 '12 at 18:08
$e^{x + i y} = e^x(\cos(y) + i \sin(y))$. –  WimC May 27 '12 at 18:10
@WimC: Thanks! Should've seen that! –  Mathmo May 27 '12 at 18:15