f(z) is analytic inside and on a closed path C. f(z) is real for all z on C.
Prove f(z) is constant.
Stuck for quite a while on this. Any help please?
Text says that this is a direct application of Rouche Theorem. Rouche's theorem is about zero's - not sure how to link that with f(z) being constant.
I was trying something on the lines that f'(z) is zero at every point. Thus f(z) is constant.
Will request any pointers here please. Thanks