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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96711] question related to (-1)^(1/3)
  • From: "һҶ֪" <lxguard-hw at yahoo.com.cn>
  • Date: Sun, 22 Feb 2009 00:33:36 -0500 (EST)

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 




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