What is the cube root of -1?

Question

kainui · Answer

Also, http://www.wolframalpha.com/input/?i=cuberoot%28-1%29%3D-1

anonymous · Answer

-1.

anonymous · Answer

Taking an odd root of a number will always give you an answer. Taking an even root of a number will give you an answer only for a positive number. Negative numbers wouldn't work unless you're doing complex numbers.

kainui · Answer

Not entirely what I'm looking for, you see that link there? The real answer is:$$\frac{ 1 }{ 2}+i \frac{ \sqrt{3} }{ 2}$$

So what's the major distinction here that wolfram alpha would say that cube root of -1 is not -1?

anonymous · Answer

I didn't get that. It said -1.

kainui · Answer

I typed that in, and it said, "False".

hartnn · Answer

there are 3 cube roots of -1 
-1 and 2 complex roots.
roots of the equation x^3+1=0

anonymous · Answer

Ah okay. And yeah hartnn beat me to it.

hartnn · Answer

wolf goes insane sometimes and produces incorrect/complicated answers...

kainui · Answer

Fair enough. It's just a computer, just making sure I wasn't missing some interesting detail of mathematics going on behind the scenes.