- #1
blahblah8724
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If [itex] z = x + iy [/itex] then the function [itex] f(z) := x^2 + iy^2 [/itex], has total derivative,
[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!
[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!