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If 1, ω, ω^2 are the cube roots of unity, then Δ = | 1 ω^n ω^(2n) ; ω^n ω^(2n) 1 ; ω^(2n) 1 ω^n | is equal to

1. ω^2
2. 0
3. 1
4. ω

Correct answer: 1

Solution

The determinant Δ represents the volume of the parallelepiped formed by the vectors corresponding to the cube roots of unity, which are symmetrically arranged in the complex plane. Since these roots are evenly spaced on the unit circle, the determinant evaluates to 1, indicating that the vectors form a complete basis in the complex space.

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