Abs and derivative problems

*To*: mathgroup at smc.vnet.net*Subject*: [mg14639] Abs and derivative problems*From*: "sylvan" <scd at gopher.chem.wayne.edu>*Date*: Wed, 4 Nov 1998 13:47:07 -0500*Organization*: Wayne State University*Sender*: owner-wri-mathgroup at wolfram.com

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 ?? I included an example below (cell format, you can cut and paste). Also, replacement rules like //. z[t_] -> t^2 do not work well on expressions like z'[t] + b z[t]. the result is z'[t] + b t^2... I could not force it to Evaluate z'[t] or D[z[t], t]. Could you help ?? I am sure there is a non-intuitive solution to that. Cell[OutputFormData["\<\ Abs[(b0*\\[CapitalDelta]z* (Es - I*\\[Eta]*\\[Omega]))/ (-I*m*\\[Gamma]*\\[Omega] + m*\\[Omega] + b0*(Es - I*\\[Eta]*\\[Omega]) - m*\\[Omega]^2)]\ \>", "\<\ Abs[(b0 \[CapitalDelta]z (Es - I \[Eta] \[Omega])) / 2 (-I m \[Gamma] \[Omega] + m \[Omega] + b0 (Es - I \[Eta] \[Omega]) - 2 m \[Omega]0 )]\ \>"], "Output", CellLabel->"Out[110]//TextForm=", LineSpacing->{1, 0}]

**Follow-Ups**:**Re: Abs and derivative problems***From:*Daniel Lichtblau <danl>