I`m confused about this problem: Let G be a bounded region in C whose boundary consists of n circles. Suppose that f is a non-constant function analytic on G: Show that if absolute value of f(z) = 1 for all z in the boundary of G then f has at least n zeros (counting multiplicities) in G.
What does it mean that boundary consists of n circles? How can I start solving the problem? Any help please...