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January 26th, 2017, 11:40 PM   #1
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Harmonic Function problems with log|f(z)|

Hi guys, any help would be appreciated!!

Suppose that f is analytic and nonzero in a domain D. Prove that log|f(z)| is harmonic in D. Use this to find a harmonic function φ(x,y) in the annulus {z : 1 ≤ |z| ≤ 2} such that φ = 1 on {|z| = 1} and φ = 2 on {|z| = 2}.
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