When I use Solve to solve for the roots of [itex]x^6+1=0[/itex], Mathematica returns the following roots:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]i[/tex]

[tex]-i[/tex]

[tex](-1)^{\frac{1}{6}[/tex]

[tex]-(-1)^{\frac{1}{6}}[/tex]

[tex](-1)^{\frac{5}{6}}[/tex]

[tex]-(-1)^{\frac{5}{6}}[/tex]

I realize these are derived from the nth roots of unity but I don't understand how Mathematica is assigning the various roots to the various fractional powers of 1/6 and 5/6. For example, if I had used [itex]x^7[/itex], then Mathematica returns values of -1 raised to 4/7, 5/7, and 6/7. How do I know what n-th root is being assigned to the power of 4/7 for example. I know I can evaluate it via N[] but I'd like to know the assignment scheme.

Anyone know?

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# A question about Mathematica

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