Complex Analysis: Theory and Applications · Problem 9.1.4

Conformal Mapping — Howell & Matthews

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

Problem

Consider the mapping

w = z^{\frac{1}{2}}

, where

z^{\frac{1}{2}}

denotes the principal branch of the square root function. If

a > 0

and

b > 0

, show that the lines

x = a

and

y = b

are mapped onto orthogonal curves.