If a = cos\(\frac{4π}{3}\) + isin\(\frac{4π}{3}\), then \(\begin{vmatrix}1 & 1 & 1 \\ 1 & a & a^2 \\ 1 & a^2 & a \end{vmatrix}\) is equal to which of the following?

Purely real Purely imaginary 0 None of these

Purely imaginary

a = cos\(\frac{4π}{3}\) + isin\(\frac{4π}{3}\) = ω2  ∴ \(\begin{vmatrix}1 & 1 & 1 \\ 1 & ω^2 & ω \\ 1 & ω & ω^2 \end{vmatrix}\) = 3(ω - ω2) purely imaginary