Complex Analysis: Theory and Applications · Problem 9.3.6

Applications of Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · conformal-mapping-exercise

Problem

Show that

w = \frac{2 - z^2}{z^2}

maps the portion of the right half-plane

\operatorname{Re}(z) > 0

that lies to the right of the hyperbola

x^2 - y^2 = 1

onto the unit disk

|w| < 1