Complex Analysis: Theory and Applications · Problem 9.3.11

Applications of Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · conformal-mapping-exercise

Problem

Show that the function

w = \frac{(1+z)^2}{(1-z)^2}

maps the portion of the disk

|z| < 1

that lies in the first quadrant onto the portion of the upper half plane

\operatorname{Im}(w) > 0

that lies outside the unit disk.