This particular problem is giving me some trouble: Suppose that f is an entire function and Re[f(z)] is less than or equal to c for all z. Show that f is constant.
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Originally Posted by spoon737 This particular problem is giving me some trouble: Suppose that f is an entire function and Re[f(z)] is less than or equal to c for all z. Show that f is constant. This is a famous famous theorem. In fact it gives a super short proof of the fundamental theorem of algebra. Here. By the actual theorem is stated and proven. Here.
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