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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: ownerwrimathgroup 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 nonintuitive 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}]
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