Question

Calcule
(-√6 - i√2) ^ 10

Answer 1

Tirando 2√2 em evidência, ficamos
{2√2·[(–√3)/2 + (cos (5π/6) + i·sen(5π/6))^10
pela fórmula de De Moivre
2^10·2{10/2}·(cos10· (5π/6) + i·sen10· (5π/6)) = 2^10·2^5·(cos(50π/6) + i·sen(50π/6)) = 2^{10 + 5} ·(cos(25π/3) + i·sen(25π/3)) = 2^15·(cos(π/3) + i·sen(π/3)) = 2^15·(1/2 + i·(√3/2)) = 2^{15 – 1}·(1 + i·√3) = 2^14·(1 + i·√3) = 2^{14} + i·2^{14}·√3