Complex Analysis: Theory and Applications · Problem 9.2.10

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · bilinear-transformations

Problem

Show that the transformation w=i+zi−zw = \dfrac{i+z}{i-z} maps the unit disk ∣z∣<1|z| < 1 onto the right half-plane Re⁡(w)>0\operatorname{Re}(w) > 0.

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