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I was never clear n this point: given that z is a single complex variable,

how/why does it make sense to talk about z having partial derivatives.?

I mean, if we are given, say, f(x,y); R<sup>2</sup> -->R<sup>n</sup>

then it makes sense to talk about f<sub>x</sub> and f<sub>y</sub>, since

x and y are different variables. But , in f(z), z is a single variable, so there are no

additional variables to refer to, to meaningfully talk about partial derivatives.

Is it the case that a function of a complex variable z is also a function of two complex

variables.?. If not, is there a formal/theoretical argument to support this use.?

Thanks.

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# Partial Derivatives for Functions f(z) of a Complex Variable.

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