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Question

Let a, b, c be complex numbers such that a + b + c = ab + ac + bc = abc = 1.Enter the values a, b, c, separated by commas, in any order.

Accepted Answer

By Vieta's formulas, a, b, and c are the roots of x^3 - x^2 + x - 1 = 0.We can write this as x^2 (x - 1) + (x - 1) = 0, or (x - 1)(x^2 + 1) = 0. The roots are 1,i,-i.