Question: Let f : U C(complex) be holomorphic, where U is an open and convex subset of C. Here, U 'convex' means that, for any two

Let f : U C(complex) be holomorphic, where U is an open and convex subset of C. Here, U 'convex' means that, for any two points in U, the whole segment determined by them lies in U.

Assume that |f(z)| K for all z U. Show that |f(z) f(w)| K|z w| for all z,w U.

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