Complex Analysis: Theory and Applications · Problem 6.1.2

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · complex-integrals-orthogonality

Problem

Let

m

and

n

be integers. Show that

\int_0^{2\pi} e^{imt}e^{-int}\,dt = \begin{cases} 0, & \text{when } m \neq n;\\ 2\pi, & \text{when } m = n. \end{cases}