A First Course in Complex Analysis · Problem 33

Isolated Singularities and the Residue Theorem — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · argument-principle

Problem

Suppose that

f(z)

has exactly one zero, at

a

, inside the circle

\gamma

, and that it has multiplicity

1

. Show that

a = \frac{1}{2\pi i} \int_\gamma \frac{z\, f'(z)}{f(z)}\, dz.