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Re: Abs and derivative problems

  • To: mathgroup at
  • Subject: [mg14650] Re: [mg14639] Abs and derivative problems
  • From: Daniel Lichtblau <danl>
  • Date: Sat, 7 Nov 1998 02:10:00 -0500
  • References: <>
  • Sender: owner-wri-mathgroup at

sylvan wrote:
> I could not calculate the modulus of  a complex expression containing
> imaginary parts in both denominator and numerator with Mathematica. An
> Example:
> (a + I b) / (c + I d)
> a,b,c,d (real) symbolic variables.
> In pratice, this should be absolutely trivial. ComplexExpand is not
> effective.
> How do you "tell" mathematica that your variables are real ??
> ...

In[19]:= ComplexExpand[Abs[(a + I b) / (c + I d)],
TargetFunctions->{Re,Im}] // InputForm

Out[19]//InputForm= Sqrt[a^2 + b^2]/Sqrt[c^2 + d^2]

The TargetFunction option is needed to tell ComplexExpand not to use Abs
(or any of Arg, Sign, or Conjugate, for that matter). Otherwise it will
simply return a result that is correct but in terms of Abs, which,
presumably, you do not want.

Daniel Lichtblau
Wolfram Research

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