1. The problem statement, all variables and given/known data Show ln(az) where a is a real number and z = x + iy is harmonic everywhere except z = 0. 2. Relevant equations z = x + iy = rcos(θ) + irsin(θ) = re^iθ z = u(x,y) + iv(x,y) Cauchy Riemann test for analyticity: ∂u/∂x = ∂v/∂y ∂u/∂y = -∂v/∂x 3. The attempt at a solution ln(az) = ln (rcos(θ) + irsin(θ)) = ln(rcos(θ+2nπ) + irsin(θ+2nπ)) = ln(a*re^iθ) = ln(ar) + i(θ+2nπ) <- this is multivalued, not harmonic. How do I show it is harmonic?