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.