       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//TextForm=",
LineSpacing->{1, 0}]

```

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