Complex Analysis: Theory and Applications · Problem 3.2.12

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · analytic-functions-differ-by-constant

Problem

Let

f

and

g

be analytic functions in the domain

D

. If

f'(z) = g'(z)

for all

z

D

, then show that

f(z) = g(z) + C

, where

C

is a complex constant.