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Re: ComplexExpand confusion


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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