Complex Analysis: Theory and Applications · Problem 6.6.2

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · maximum-modulus-principle

Problem

Let

f(z) = az^n + b

, where the region is the disk

R = \{z : |z| \leq 1\}

. Show that

\displaystyle\max_{|z|\leq 1}|f(z)| = |a| + |b|