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MathGroup Archive 2005

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Re: ComplexExpand confusion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60135] Re: [mg60109] ComplexExpand confusion
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sun, 4 Sep 2005 03:01:58 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

The Further Examples for ComplexExpand states that it will expand complex 
powers, i.e., it is converting from the polar form of the complex number to its 
Cartesian form.

(-1)^(1/4)//ComplexExpand

(1 + I)/Sqrt[2]

%//FullSimplify

(-1)^(1/4)

You get the same result with ExpToTrig

(-1)^(1/4)//ExpToTrig

(1 + I)/Sqrt[2]


Bob Hanlon

> 
> From: mike_in_england2000 at yahoo.co.uk
To: mathgroup at smc.vnet.net
> Date: 2005/09/03 Sat AM 02:05:58 EDT
> Subject: [mg60135] [mg60109] ComplexExpand confusion
> 
> 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
> 
> 


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