Re: Abs and derivative problems

*To*: mathgroup at smc.vnet.net*Subject*: [mg14650] Re: [mg14639] Abs and derivative problems*From*: Daniel Lichtblau <danl>*Date*: Sat, 7 Nov 1998 02:10:00 -0500*References*: <199811041847.NAA19370@smc.vnet.net.>*Sender*: owner-wri-mathgroup at wolfram.com

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

**References**:**Abs and derivative problems***From:*"sylvan" <scd@gopher.chem.wayne.edu>