Complex Analysis: Theory and Applications · Problem 2.5.5

Analytic and Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · reciprocal-transformation

Problem

Find the image of the disk

D_{\frac{4}{3}}\!\left(-\frac{2i}{3}\right) = \left\{z : \left|z + \frac{2i}{3}\right| < \frac{4}{3}\right\}

under

f(z) = \frac{1}{z}