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MathGroup Archive 2006

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RE: Is -1^(2/5) really undefined in R?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69105] RE: [mg69075] Is -1^(2/5) really undefined in R?
  • From: "Jaccard Florian" <Florian.Jaccard at he-arc.ch>
  • Date: Wed, 30 Aug 2006 06:33:09 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello Ben,

I suppose you ment (-1)^(2/5) ?

If yes, I'm afraid your equalities are wrong.

1^(2/5)=1,

But 

(-1)^(2/5)=(1*E^(I*Pi))^(2/5)=(1^(2/5))*E^(I*2*Pi/5)=E^(2IPi/5)=Cos[2Pi/5]+I*Sin[2Pi/5] 

Is a complex number!

Regards

Florian Jaccard
florian.jaccard at he-arc.ch
-----Message d'origine-----
De : Ben [mailto:ben.carbery at spam.me] 
Envoyé : mardi, 29. août 2006 10:48
À : mathgroup at smc.vnet.net
Objet : [mg69075] Is -1^(2/5) really undefined in R?

Is -1^(2/5) really undefined in R?

Mathematica seems to think so, I guess since it looks like a negative square root, but

-1^(2/5) = (-1^2)^(1/5) = 1^(1/5) = 1

Is this correct mathematically?

cheers,

BC


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