−43=−64
so the third root of −64 should be −4 than.
3√−64=−4
But if you calculate the third root of -64
with WolframAlpha( http://www.wolframalpha.com/input/?i=third+root+of+-64 )
you get a complex number with an imaginary part of 3.4641016151i and a real part of 2
so if the third root of 4−64 equals −4 AND 2+3.46410162i (which i know is a bit foolish) than you could actually reform it like this
3√−64≈2+3.46410162i|−2
3√−64−2≈−6≈3.46410162i|/3.46410162
3√−64−23.46410162≈−63.46410162≈i
and this have to be totally wrong, so my question is, where exactly is the mistake?
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