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

• To: mathgroup at smc.vnet.net
• Subject: [mg69136] Re: Is -1^(2/5) really undefined in R?
• From: dh <dh at metrohm.ch>
• Date: Wed, 30 Aug 2006 06:36:19 -0400 (EDT)
• References: <ed0uvq\$po\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```version= Mathematica 5.1, Windows

Hi Ben,

There are actually five values of -1^(2/5), one of which is real.

Consider -1=Exp[I (Pi + 2 n Pi)]. Then -1^(2/5)=Exp[2/5 I(I Pi + 2 n Pi)]

Well, which value will mathematica return. You can find the answer in

the manual under Power: "Power gives the principal value of a Exp[y

Log[x]]", this is unfortunately not 1 as you expected, but on of the

complex values.

Daniel

Ben 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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