Complex Analysis: Theory and Applications · Problem 8.7.9

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · rouche-theorem

Problem

Suppose that

h(z)

is analytic and nonzero and

|h(z)| < 1

for

z \in D_1(0)

. Prove that the function

g(z) = h(z) - z^n

has

n

zeros inside the unit circle

C_1(0)