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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