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MathGroup Archive 2004

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Re: Problem with the Derivative of a Arg-function

  • To: mathgroup at
  • Subject: [mg48512] Re: [mg48482] Problem with the Derivative of a Arg-function
  • From: Andrzej Kozlowski <akoz at>
  • Date: Fri, 4 Jun 2004 04:49:27 -0400 (EDT)
  • References: <>
  • Sender: owner-wri-mathgroup at

On 2 Jun 2004, at 17:21, Alex Klishko wrote:

> Hello group,
> Let us define a simple complex function Exp[-j*x], j is a square root 
> of -1.
> Fase of this function is computed by Arg -function.
> If x is a real number the fase is equal -x and it's derivative is -1.
> If x is a complex number the fase is equal Re[-x].
> But if we would write:
> f[x_] = Arg[E^(-j*x\)];  N[D[f[x], x]]\  /. \ x -> 5+j*3
> we would get a complex number not equal -1.
> In case of a real x, this problem may be solved by 
> ComplexExpand-function:
> f[x_] = ComplexExpand[Arg[E^(-j*x\)]];  N[D[f[x], x]]\  /. \ x -> 5
> we would get -1.
> In case of a complex x, Matematica gives a wrong solution.
> Would you correct me if I make a mistake.
> Wishes
> Alex Klishko
I am not sure what you mean by "fase"? Is that just Arg[E^(-I*x)]? Are 
you saying that this is -Re[x] for all complex x? Well, that certianly 
is not true, even for real ones!
For example


-20+6 Pi

or more famously:




    TargetFunctions -> {Re, Im}], -Pi/2 < x < Pi/2]


Maybe I have misunderstood something?

Andrzej Kozlowski
Chiba, Japan

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