Let D be a bounded domain with boundary B. Suppose that f and g are both analytic on D and continuous on DuB, and suppose further that Re f(z) = Re g(z) for all z e B. Show that ƒ = g + ia in D, where a is a real constant.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.