A First Course in Complex Analysis · Problem 2.5.28

Differentiation — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · cauchy-riemann-equations

Problem

Suppose

f

and

g

are holomorphic functions on a region

G

and

f'(z) = g'(z)

for all

z \in G

. Show that

f

and

g

differ by a constant.