Complex Analysis: Theory and Applications · Problem 2.5.6

Analytic and Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · reciprocal-transformation

Problem

Show that the reciprocal transformation maps the disk

|z - 1| < 2

onto the region that lies exterior to the circle

\left\{w : \left|w + \frac{1}{3}\right| = \frac{2}{3}\right\}