Complex Analysis: Theory and Applications · Problem 16

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · complex-definite-integrals

Problem

Let

z_1

and

z_2

be points in the right half-plane and let

C

be the line segment joining them. Show that

\int_C \frac{1}{z^2}\,dz = \frac{1}{z_1} - \frac{1}{z_2}