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Re: Re: ComplexExpand confusion


(-1)^(1/4) does not look like polar form to me!

Bob Hanlon wrote:
> 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: [mg60158] [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
>>
>>
> 
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
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University of Massachusetts                413 545-2859 (W)
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