# Homework Help: Number of zero's of holomorphic function

1. Jun 8, 2013

### hedipaldi

1. The problem statement, all variables and given/known data

Let f(z) be holomorphic in the open unit disc taking real values only on the real axis.show that f has at most one zero in the open disc.

2. Relevant equations

Rouche's theorem,the argument principle.

3. The attempt at a solution
obviously,f does not have non-real zero's .I need help in counting the zero's by using the argument principle.

Last edited: Jun 8, 2013
2. Jun 8, 2013

### Dick

I'm not an expert, but is argument is zero at +1 and -1 and can't be zero anyplace else as the contour winds around the boundary of the unit circle. What are the possibilities for the winding number?