MathsJEE Main 22 Jan 2026, Shift 1·Q21·Numerical·Moderate

Complex Numbers · Cube roots of unity

Let

\alpha = \dfrac{-1 + i\sqrt3}{2}

and

\beta = \dfrac{-1 - i\sqrt3}{2}

i = \sqrt{-1}

. If

(7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10},

then

m

is .

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