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 $Arg(z)\in (-\pi,\pi)$?
2026-03-27 03:41:09.1774582869
What is a harmonic conjugate of $u=Arg(z)$?
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Hint: $\log(z) = \log|z| + i \arg(z)$