Let z0 be a root of the quadratic equation x² + x + 1 = 0. If z = 3 + 6i(z0)^810 - i(z0)^930, then arg(z) is equal to: π/4, π/3, π/6, 0
π4
0
π3
π6
Solution:
We know that z0 = ω or ω² (where ω is a non-real cube root of unity) z = 3 + 6i(ω)^810 - i(ω)^930 z = 3 + 3i [∵ ω³ = 1] z = 3 + 3i comparing with z = x + iy ⇒ arg(z) = tan⁻¹(y/x) = π/4