Re: Re: ComplexExpand confusion

• To: mathgroup at smc.vnet.net
• Subject: [mg60158] Re: [mg60135] Re: [mg60109] ComplexExpand confusion
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Mon, 5 Sep 2005 02:27:51 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200509040701.DAA07297@smc.vnet.net>
• Reply-to: murray at math.umass.edu
• Sender: owner-wri-mathgroup at wolfram.com

```(-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
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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