Complex Analysis: Theory and Applications · Problem 9.2.5

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · bilinear-transformations

Problem

Find the image of the upper half-plane Im⁡(z)>0\operatorname{Im}(z) > 0 under the transformation w=(1−i)z+2(1+i)z+2.w = \frac{(1-i)z+2}{(1+i)z+2}.

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