Complex Analysis: Theory and Applications · Problem 2.5.11

Analytic and Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · reciprocal-transformation

Problem

Show that the transformation w=2−zz=−1+2zw = \frac{2-z}{z} = -1 + \frac{2}{z} maps the disk ∣z−1∣<1|z - 1| < 1 onto the right half-plane Re⁡(w)>0\operatorname{Re}(w) > 0.

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