Question: 1. Let u and v be two harmonic functions. Prove that a linear combination au + Bv, a, B ER, is also a harmonic

1. Let u and v be two harmonic functions. Prove that a

1. Let u and v be two harmonic functions. Prove that a linear combination au + Bv, a, B ER, is also a harmonic function. 2. Is u? a harmonic function if u is a non-constant harmonic function? Give reason for your answer. 3. Let u be a harmonic function. For what functions f is the function f(u) also harmonic? Ans: Au + B 4. Are |f(z)| harmonic functions if f(z) is an analytic function? Ans: No

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