How to find all analytic functions $f$ such that $\operatorname{Im}f(z)=g(|z|^2)$, where $g$ is a real-valued function? Cauchy-Riemann is not very helpful as $g$ is not given explicitly.
2026-03-27 10:17:04.1774606624
Recover holomorphic function $Imf(z)=g(|z|^2)$
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Hint: This would imply $\text { Im } f(z)$ is constant on the unit circle.