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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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