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MathGroup Archive 2004

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RE: Complex Numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47438] RE: [mg47425] Complex Numbers
  • From: "Florian Jaccard" <florian.jaccard at eiaj.ch>
  • Date: Mon, 12 Apr 2004 03:44:52 -0400 (EDT)
  • Reply-to: <florian.jaccard at eiaj.ch>
  • Sender: owner-wri-mathgroup at wolfram.com

ComplexExpand[expr] expands expr assuming that all variables are real.
So if you want that a and b are assumed to be real, you have first to take
the real part, and then ComplexExpand !

In[1]:=
ComplexExpand[Re[ Exp[a I] Exp[b I]]]

Out[1]=
Cos[a+b]

You often will have to use the option :

ComplexExpand[... ,TargetFunctions->{Re,Im}]

to obtain what you really want.

You can also use Simplify and tell Mathematica that all your variables are
real :

In[4]:=
Simplify[Re[Exp[a*I]*Exp[b*I]], Element[_, Reals]]

Out[4]=
Cos[a + b]

Regards

Florian Jaccard

-----Message d'origine-----
De : Alejandro Vizcarra [mailto:gebankos at prodigy.net.mx]
Envoyé : dim., 11. avril 2004 10:44
À : mathgroup at smc.vnet.net
Objet : [mg47425] Complex Numbers


Hi,:

I always have problems when dealing with complex numbers.  How can i
work with Mathematica in such a way that every expression will
be considered real unless it is declared explicitly complex (like a = 3 + 4
I ) ?

For example if I type

Re[ComplexExpand[ Exp[a I] Exp[b I]]]

I get the answer

-Im[Sin[ a+b]]+Re[Cos[a+b]]

Instead of simply Cos[a+  b]

Thnx!


Alejandro Vizcarra






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