Complex Analysis: Theory and Applications · Problem 6.6.4

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · maximum-modulus-principle

Problem

Let

f(z) = z^2

. Evaluate the following, where

R

represents the rectangular region defined by the set

R = \{z = x+iy : 2 \leq x \leq 3 \text{ and } 1 \leq y \leq 3\}.

((a))

\displaystyle\max_{z\in R}|f(z)|

. ((b))

\displaystyle\min_{z\in R}|f(z)|

. ((c))

\displaystyle\max_{z\in R}\mathrm{Re}[f(z)]

. ((d))

\displaystyle\min_{z\in R}\mathrm{Im}[f(z)]