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Prove Exponential Identity Analyticity & Congruence Corollary

Prove that e^(z+a) = (e^z)(e^a) by applying the following Corollary:

Corollary. If f and g and are analytic on a region G then f ≡ g iff {z E G : f(z)=g(z)} has a limit point in G.

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Solution Summary

An exponential identity is proven using an analyticity and congruence corollary. The solution is detailed and well presented.