Complex Analysis: Theory and Applications · Problem 6.3.2

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · cauchy-goursat-theorem

Problem

Show that

\displaystyle\int_C z^{-1}\,dz = 2\pi i

, where

C

is the square with vertices

1 \pm i

, and

-1 \pm i

and having positive orientation.