If there is a function $f: \mathbb{C} \rightarrow \mathbb{R}$, namely $ f(Z)$. Is it correct to search minima of the function by demanding $\frac{\partial f} {\partial Z}$ = 0 , where Z is a complex number?
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$\begingroup$ Welcome to MSE. Please read this text about how to ask a good question. $\endgroup$– José Carlos SantosCommented Apr 15, 2022 at 7:39
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$\begingroup$ @KaviRamaMurthy - if they had $\dfrac{df}{dz}$ that would be correct, but $\dfrac{\partial f}{\partial z}$ and its partner $\dfrac{\partial f}{\partial \overline z}$ are definable whenever $\dfrac{\partial f}{\partial x}$ and $\dfrac{\partial f}{\partial y}$ exist, where $z = x+iy$. $\endgroup$– Paul SinclairCommented Apr 16, 2022 at 2:59
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