What is a harmonic conjugate of $u=Arg(z)$?

Question

Let $u=Arg(z)$ be a function maps $\mathbb{C}\setminus \{0\}$ to $ (-\pi,\pi]$.

How do i find a harmonic conjugate of $u$ when $Arg(z)\in (-\pi,\pi)$?

This question was also asked and answered here. – Dean Gurvitz Nov 16 '17 at 09:44 — Dean Gurvitz, Nov 16 '17 at 09:44
This question was also asked and answered here. – Dean Gurvitz Nov 16 '17 at 09:47 — Dean Gurvitz, Nov 16 '17 at 09:47

score 0 · Accepted Answer · answered Apr 21 '14 at 18:30

0

Hint: $\log(z) = \log|z| + i \arg(z)$

answered Apr 21 '14 at 18:30

Seth

1 Answers1