Cube Root of Unity Equation (Jee Mains)

Algebra and Representation of Complex Numbers

Hard

Cube Root of Unity Equation

Let α be a solution of x² + x + 1 = 0, and for some a and b in

, [4 a b] $\left[ {\begin{array}{*{20}{c}} 1&{16}&{13}\\[0.9em] { - 1}&{ - 1}&2\\[0.9em] { - 2}&{ - 14}&{ - 8} \end{array}} \right]$ = [0 0 0]. If $\frac{4}{{{\alpha ^4}}}$ + $\frac{m}{{{\alpha ^a}}}$ + $\frac{n}{{{\alpha ^b}}}$ = 3, then m + n is equal to ___

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