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Re: Absolute Value of Complex Numbers
*To*: mathgroup at smc.vnet.net
*Subject*: [mg35203] Re: [mg35196] Absolute Value of Complex Numbers
*From*: BobHanlon at aol.com
*Date*: Tue, 2 Jul 2002 02:11:57 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
In a message dated 7/1/02 3:52:13 AM, kyledavis at nowhere.com writes:
>Abs[2 Exp[3 * i]]
>answer = 2
>
>Abs[2 Exp[k * i]]
>answer = 2 Exp[-Im[k]]
>
>Isn't the second answer supposed to be the same with the first one,
>regardless with the value of k? How do I make the second calculation give
>me
>the right answer?
>
You apparently intend for k to be real. You must convey that to Mathematica.
Clear[k];
If all variables are real then use ComplexEpand
{Abs[2 Exp[k*I]], Abs[2 Exp[k*I]] // ComplexExpand}
{2/E^Im[k], 2}
If specific variables are real then use an assumption with Simplify or
FullSimplify
{Abs[2 Exp[k*I]], Simplify[Abs[2 Exp[k*I]], Element[k, Reals]]}
{2/E^Im[k], 2}
or explicitly set the imaginary part to zero.
k /: Im[k] = 0;
Abs[2 Exp[k*I]]
2
See also the standard add-on package Algebra`ReIm`
Bob Hanlon
Chantilly, VA USA
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