A First Course in Complex Analysis · Problem 32

Integration — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · complex-exponential

Problem

Describe the images of the following sets under the exponential function

\exp(z)

: ((a)) the line segment defined by

z = iy

0 \leq y \leq 2\pi

((b)) the line segment defined by

z = 1 + iy

0 \leq y \leq 2\pi

((c)) the rectangle

\{z = x + iy \in \mathbb{C} : 0 \leq x \leq 1,\ 0 \leq y \leq 2\pi\}