Is $e^z + \overline{z}^2$ holomorphic?

Question

Can a sum of a holomorphic and non-holomorphic functions be itself holomorphic? As I understand, $\overline{z} ^2$ is not holomorphic?

If it was then the non-holomorphic function would be the difference of two holomorphic functions which is holomorphic. — copper.hat, Jun 20 '13 at 18:38

score 12 · Accepted Answer · answered Jun 20 '13 at 18:33

12

The difference of two holomorphic functions is holomorphic. Is $(e^z + \bar z^2) - e^z$ holomorphic?

answered Jun 20 '13 at 18:33

Umberto P.

Thanks for your answer. I calculated $\overline{z} ^2$ is not holomorphic because it doesn't satisfy the C-R conditions. – Spine Feast Jun 20 '13 at 18:57

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