A First Course in Complex Analysis · Problem 2.5.20

Differentiation — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · harmonic-functions

Problem

Suppose

f = u + iv

is holomorphic in the region

G

. Show that the following functions are harmonic in

G

: ((a))

u

((b))

v

((c))

|f|^2 = u^2 + v^2