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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: [mg69086] Re: [mg69075] Is -1^(2/5) really undefined in R?
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Wed, 30 Aug 2006 06:32:11 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

It appears that you mean (-1)^(2/5)

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

-(1/4) + Sqrt[5]/4 + (1/2)*I*Sqrt[(1/2)*(5 + Sqrt[5])]

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

0.30901699437494745 + 0.9510565162951536*I

Plot[{Re[x^(2/5)],Im[x^(2/5)]},{x,-2,0},
    PlotStyle->{Blue,Red}];

Plot[{Re[(-1)^x],Im[(-1)^x]},{x,0,1},
    PlotStyle->{Blue,Red}];


Bob Hanlon

---- Ben <ben.carbery at spam.me> wrote: 
> 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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