Complex Analysis: Theory and Applications · Problem 9.1.3

Conformal Mapping — Howell & Matthews

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

Problem

Consider the mapping

w = z^2

. If

a \neq 0

and

b \neq 0

, show that the lines

x = a

and

y = b

are mapped onto orthogonal parabolas.