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Problem with the Derivative of a Arg-function

• To: mathgroup at smc.vnet.net
• Subject: [mg48482] Problem with the Derivative of a Arg-function
• From: klishko at mail.ru (Alex Klishko)
• Date: Wed, 2 Jun 2004 04:21:47 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: Problem with the Derivative of a Arg-function
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>