Complex Analysis: Theory and Applications · Problem 2.5.4

Analytic and Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · reciprocal-transformation

Problem

Show that the reciprocal transformation

w = \frac{1}{z}

maps the vertical strip

0 < x < \frac{1}{2}

onto the region in the right half-plane

\operatorname{Re}(w) > 0

that is outside the disk

D_1(1) = \{w : |w-1| < 1\}