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NVAMediumJEE Main 2026 · 22 January, Shift 1Complex Numbers Basics

Mathematics Question from JEE Main 2026 · 22 January, Shift 1

Let α=−1+i32\alpha = \dfrac{-1 + i\sqrt{3}}{2} and β=−1−i32\beta = \dfrac{-1 - i\sqrt{3}}{2}, where i=−1i = \sqrt{-1}. If

(7−7α+9β)20+(9+7α−7β)20+(−7+9α+7β)20+(14+7α+7β)20=m10(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 the value of mm is _____.

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