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MathGroup Archive 2002

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Re: Absolute Value of Complex Numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35202] Re: Absolute Value of Complex Numbers
  • From: "Allan Hayes" <hay at haystack.demon.co.uk>
  • Date: Tue, 2 Jul 2002 02:11:55 -0400 (EDT)
  • References: <afp0oh$h08$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Kyle Davis" <kyledavis at nowhere.com> wrote in message
news:afp0oh$h08$1 at smc.vnet.net...
> 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?

Only if k is real, but Mathematica allows for other values, for example

    Abs[2 Exp[I* I]]

    2/E

The general result is if k = x+I y then we get Abs[2 Exp[(x+I y)] =  2 Abs[
Exp[-y+ I x] ] = Abs[Exp[y] Exp[I x]] = Abs[Exp[-y]] = Exp[-y]]

>How do I make the second calculation give me the right answer?

    Simplify[Abs[2 Exp[k * I]], Element[k, Reals]]

    2

--
Allan

---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565


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