Exercise 9.   Suppose that    is analytic and nonzero and     for   .  

Prove that the function      has  n  zeros inside the unit circle  .  

Solution 9.

Solution.   Let  .   Then for    we have

            

Since    has n zeros in  ,  then    has n zeros inside the unit circle  ,  by Remark 8.5 to Rouché's Theorem.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell