If [itex] z = x + iy [/itex] then the function [itex] f(z) := x^2 + iy^2 [/itex], has total derivative,(adsbygoogle = window.adsbygoogle || []).push({});

[itex] \begin{pmatrix} 2x & 0 \\ 0 & 2y \end{pmatrix} [/itex]

so surely by the Cauchy–Riemann equations this is complex differentiable at [itex] x = y [/itex], but is this function holomorphic anywhere?

Thanks!

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# Is this function holomorphic?

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