Prove rigorously that the functions $f(z)$ and $\overline{f(\overline{z})}$ are simultaneously analytic.
From where do i start and what does simultaneouslt means here?
Any help is appreciated ?
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$f$ is analytic on $U\subseteq_{\text{open}}\Bbb C\iff z\mapsto \overline{f(\overline z)},z\in \overline U:={\overline z\in \Bbb C| z\in U}$ is analytic. – Sumanta Nov 14 '19 at 09:01
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I just started complex analysis so it would be better if you explain in simple terms – AKA Death Nov 14 '19 at 09:02
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"Simultaneously" means what that duplicate question says. But using the word "simultaneously" like this can be confusing, and should be avoided. – GEdgar Nov 14 '19 at 09:55