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Re: Derivative of g(z) = Arg(z) and f(z) = Re(z) + Im(z)?
Marie wrote: > How do I solve a derivative of a complex function Arg(z) or Re(z) + > Im(z) by definition? (f(z) - f(w))/(z-w) -> f'(w) as z->w... Let f(z) = P + I Q be the value of a complex function. I remember that if P is constant and Q variable (or P variable and Q constant) then f can't be complex differentiable because the Cauchy-Riemann conditions can't be met. Hence Arg, Re, Im, Abs are not complex differentiable. Curiously, Mathematica [5.0] doesn't refuse to evaluate Arg' : In:= Arg'[1 + 2 I] // N Out= -0.4 Valeri