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## Homework Statement

Without directly verifying via the laplace equations, explain why Log|z| is harmonic in the punctured complex plane.

## Homework Equations

## The Attempt at a Solution

I thought it was because Log z is analytic on the complex plane except for the nonpositive real axis, so Log |z| would be analytic and hence harmonic since any |z| turns z into a positive real (for z=/= 0), hence Log |z| is like Log z for positive reals. But, if it's that, why would they ask to show its harmonic and not analytic.