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MathGroup Archive 2005

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Re: ComplexExpand confusion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60132] Re: ComplexExpand confusion
  • From: "Scout" <not at nothing.net>
  • Date: Sun, 4 Sep 2005 03:01:55 -0400 (EDT)
  • References: <dfbejf$im2$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

<mike_in_england2000 at yahoo.co.uk>
> Hi
>
> The Mathematica help system says that
>
> "ComplexExpand[expr] expands expr assuming that all variables are
> real."
>
> which is fine and explains why expressions such as
> ComplexExpand[Conjugate[x +I y]] work.All seems obvious so far.
>
> What is confusing me though is why does
>
> ComplexExpand[(-1)^(1/4)]
>
> give the result
>
> (1 + I)/Sqrt[2]
>
> I know this the correct result but in the expression (-1)^(1/4) there
> are no variables.  The numbers involved are real so what on earth is
> ComplexExpand doing? Is this a stupid question? Should I have drank
> more coffee before posting this.
>
> Thanks
> Mike
>

(-1)^(1/4) is an EXPRESSION that has "no sense" in Reals but it's defined 
only in the Complex domain...

    ~Scout~


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