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Re: Very strange Bug !?

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  • Subject: [mg13154] Re: [mg13037] Very strange Bug !?
  • From: Hugh Walker <hwalker at>
  • Date: Mon, 13 Jul 1998 07:42:06 -0400
  • Sender: owner-wri-mathgroup at

On 7Jul98 M Blle Ramquet <MN.Ramquet at> wrote:

" I just discovered something that amazed me. If you type

N[(-1)^{1/3}], it gives an imaginary answer !!! I've tried it out with
an old local release but it is still the same. Of course the problem is
the same for all cubic root of any negative number... I know that
purely, the root of a negative real is not well defined ... but anyway
it is commonly accepted that (-1)^{1/3} is -1 !!!

  Can any guru of mathematica help me to sort out this mess ?"

I find, using v. 3.0, the (expected) Mathematica result

(-1)^(1/3) -> (-1)^(1/3)

and also the principal value

(-1)^(1/3)//ComplexExpand -> (1/2) + I Sqrt[3]/2

I also get

(-1)^(1/3)//N -> 0,5 + I 0,866025

These conform with what I understand about the rules of complex

Hugh Walker
Professsor Emeritus
University of Houston

Gnarly Oaks

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