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Prove the following (Corollary 7.9 from Bak and Newman's Complex analysis book.) If f is analytic in a region symmetric with respect to the real

Prove the following (Corollary 7.9 from Bak and Newman's Complex analysis book.)

If f is analytic in a region symmetric with respect to the real axis and if f is real for real z, then f (z) = f(2)

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