Complex Analysis: Theory and Applications · Problem 9.1.6

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · conformal-mappings-orthogonal-images

Problem

For

w = \sin z

show that the line segment

-\dfrac{\pi}{2} < x < \dfrac{\pi}{2}

y = 0

, and the vertical line

x = a

, where

|a| < \dfrac{\pi}{2}

, are mapped onto orthogonal curves.