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I need help with this problem. Problem 1. {10 points] Let ag} and rim, 3;} be a conjugate pair of smooth harmonic functions in a

I need help with this problem.

Problem 1. {10 points] Let ag} and rim, 3;} be a conjugate pair of smooth harmonic functions in a domain D. Prove that a" nzez + v4 is a harmonic function in D. Find all possible harmonic conjugates of 1:" E's-Fug + 11"

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