A First Course in Complex Analysis · Problem 2.5.10

Differentiation — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · continuity-complex-functions

Problem

Suppose

f

and

g

are continuous on

G \subseteq \mathbb{C}

. Prove that the following functions are also continuous on

G

: ((a))

f(z) + g(z)

((b))

f(z) \cdot g(z)

((c))

f(z) / g(z)

(at points where

g(z) \neq 0

) ((d))

|f(z)|

((e))

\overline{f(z)}