Complex Analysis: Theory and Applications · Problem 9.4.15

Applications of Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · trigonometric-mapping-exercise

Problem

Show that the transformation

w = \sin^2 z

is a one-to-one conformal mapping of the semi-infinite strip

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

y > 0

, onto the upper half plane

\operatorname{Im}(w) > 0