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Let $f(z)$ analytic. Prove that $\overline{ f(\bar{z})}$ is also analytic.

How do I use the concept of analytic of $f(z)$ here? any help

Chappers
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Eklavya
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1 Answers1

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Use the series expansion of $f$ around a point. If you conjugate $z$ first and then $f$, the coefficients are conjugated and you still have a series expansion around each point.

Pedro
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  • how to put bar on $f(\bar{z})$?? by which command ? – Eklavya Jan 18 '16 at 19:26
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    @Eklavya \overline{f(z)} gives $\overline{f(z)}$. The \overline{} command adapts to the length of the argument, so for example you can get $\overline{z_1+z_2+z_3+z_4}$ using \overline{z_1+z_2+z_3+z_4}. – Pedro Jan 18 '16 at 19:34