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Re: question related to (-1)^(1/3)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96732] Re: [mg96711] question related to (-1)^(1/3)
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Mon, 23 Feb 2009 05:01:49 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200902220533.AAA12584@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

No, because (-1)^(1/3) is NOT -1.  Rather, it is the principal cube-root 
of -1.

=D2=BB=D2=B6=D6=AA=C7=EF wrote:
> I have tried expression:
> RecurrenceTable[{x[n + 1] == -x[n]^(1/3), x[0] == 1},
>   x, {n, 1, 200}] // N
>
> Mathematica produce
>  {-1., -0.5 - 0.866025 I, -0.766044 + 0.642788 I, -0.686242 -
>   0.727374 I, -0.71393 + 0.700217 I, -0.704818 - 0.709389 I,
> ...
>
> But it should be {1, -1, 1, -1, ... }
>
> If you try  (-1)^(1/3)
>
> In[10]:= (-1)^(1/3)
>
> Out[10]= (-1)^(1/3)
>
> In[11]:= % // N
>
> Out[11]= 0.5 + 0.866025 I
>
>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305



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