A First Course in Complex Analysis · Problem 6.3.2

Power Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · harmonic-functions

Problem

Suppose

u(x,y)

and

v(x,y)

are harmonic in

G

, and

c \in \mathbb{R}

. Prove that

u(x,y) + c\,v(x,y)

is also harmonic in

G