Sorry if this question was asked before... I was searching and I dont found something about that.
Suppose that I have a function on the complexes, that is $f:\Bbb C\to\Bbb C$, and I want to evaluate it (total) derivative. I know that I can write the function as a function in $\Bbb R^2$ of the kind $f\mapsto g:=(\Re(f),\Im(f))$, and after see if the function $g$ is totally differentiable and, when it happen, if the Cauchy-Riemann equations holds to see if the original function $f$ is complex differentiable in this region.
But probably there is some shortcut to this workaround, and this is what Im searching for.
EDIT: because some trolls voted to close this question by the supposed reason that "this is not related to the Wolfram mathematical software" I must declare that I want a way to evaluate the derivative of a complex function in Wolfram Mathematica, of course! :)
By example the following code
f[z_]:= D[z^2,z]
when called after, by example for f[3+I] says that 3+Iis not a correct variable. So I must found other method.
Assuming. e.g.,Assuming[z ~Element~ Complexes, D[z^2, z]]. Also maybe give the intro tutorials a look.f[3+I]insert3+Ianywhere it seesz. So that expanded toD[(3+I)^2, 3+I]which is, of course, an improper usage ofD. Note thatD[(3 + I)^2, z]works. – b3m2a1 Sep 04 '17 at 04:46Clear[f, x, z]; f[z_] = D[x^2, x] /. x -> zand thenf /@ {x, z, 3 + I}will evaluate the way we want. But ifxandzalready have values that cannot be cleared, another method isClear[f]; f[z_] := Module[{x}, D[x^2, x] /. x -> z], and thenf/@{x, z, 3+I}will evaluate the way we want. Note the use ofSetin the first method andSetDelayedin the second method. – LouisB Sep 04 '17 at 05:45