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Manipulating a complex modulus expression

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82860] Manipulating a complex modulus expression
  • From: carlos at Colorado.EDU
  • Date: Thu, 1 Nov 2007 05:21:21 -0500 (EST)

Could somebody explain why Mathematica does not
return the same expression in the following cases.
Version: 5.2 on Mac OSX 10.4.9.
Let

  d=(Abs[-1+x+I*y])^2;

The following 3 statements should be equivalent, since the
documentation says that ComplexExpand assumes that all
variables are real:

  s=ComplexExpand[d];                       Print[s];
  s=Simplify[d,x=E2=88=88Reals&&y=E2=88=88Reals];     Print[s];
  s=FullSimplify[d,x=E2=88=88Reals&&y=E2=88=88Reals]; Print[s];

All should return  (-1+x)^2+y^2.   But only the last one does.
Make a slight change:

  d=1/(Abs[-1+x+I*y])^2;

Now none of the 3 returns 1/ ((-1+x)^2+y^2) . Why?



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