Complex Numbers Power Calculation (Jee Mains)

Algebra and Representation of Complex Numbers

Medium

Complex Numbers Power Calculation

Let $\alpha = \frac{{ - 1 + i\sqrt 3 }}{2}$ and $\beta = \frac{{ - 1 - i\sqrt 3 }}{2}$ , $i = \sqrt { - 1}$ . If (7 – 7α + 9β)²⁰ + (9 + 7α – 7β)²⁰+ (–7 + 9α + 7β)²⁰+ (14 + 7α + 7β)²⁰ = m¹⁰, then m is ________.