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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2010 • Question 6

Question

Math 6210 • Real Analysis Fall 2010 • Question 6

Let \[ f(z)=1-\cos z. \] (i) Find all zeros of this function;

(ii) Find the multiplicities of these zeros.

Raw LaTeX

Let
\[
f(z)=1-\cos z.
\]
(i) Find all zeros of this function;

(ii) Find the multiplicities of these zeros.

Topic Tags

Zeros of Holomorphic Functions and the Identity Theorem