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Analytic function proof

Let f = u + iv be an analytic function on an open connected set G in C ( C = complex plane) where u and v are its real and imaginary parts. assume u(z) >= u(a) for some a in G and all z in G. Prove that f is constant.

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Proof:

Let g(z)=exp(-f(z)). Since for all z in G, we have u(z)>=u(a) for some a in G, then we ...

Solution Summary

This is a proof regarding an analytic function on an open connected set.

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