A First Course in Complex Analysis · Problem 51

Integration — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · complex-exponential

Problem

Describe the image under

\exp

of the line with equation

y = x

. To do this you should find an equation (at least parametrically) for the image (you can start with the parametric form

x = t

y = t

), plot it reasonably carefully, and explain what happens in the limits as

t \to \infty

and

t \to -\infty