# Can Mathematica give the solutions to x^n - 1 = 0 in their radical form [duplicate]

If I input:

Solve[x^3 - 1 == 0]


Mathematica returns:

{{x -> 1}, {x -> -(-1)^(1/3)}, {x -> (-1)^(2/3)}}

I want to see the roots expressed as radicals for example:

1/2 + Sqrt(-3)/2

• Have you tried ComplexExpand? I'm not sure it does what you want for high order roots. FunctionExpand will expand them if they can be expressed in terms of square roots (see this). – Michael E2 Mar 12 '16 at 17:36
• Try ExpToTrig[] and report back. – J. M.'s torpor Mar 12 '16 at 17:43
• It appears that ExpToTrig and ComplexExpand will return all the solutions of x^n -1 ==0 in radicals for n < 7. Table[ExpToTrig[Solve[x^n - 1 == 0][[All, 1, 2]]], {n, 1, 10}] – Geoffrey Critzer Mar 12 '16 at 18:24