Anonymous

ω⁴⁴ + ω⁴⁵ = ω² + 1 as ω³ = 1, and as 1 + ω + ω² = 0 we have... ω⁴⁴ + ω⁴⁵ = ω² + 1 = 0 - ω = -ω which isn't any of those answers, but we can... ω⁴⁴ + ω⁴⁵ = ω² + 1 = 0 - ω = -ω = -ω/1 = -ω/ω³ = -1/ω² = 1/(-ω²), so yes, Answer C

Anonymous

w^3 = 1, w^44 + w^45 = ? w^44 + w^45 = w^45 / w + w^45 = (w^3)^15 / w + (w^3)^15 w^3 = 1 => (1)^15 / w + (1)^15 = 1/w + 1 None of options

Anonymous

w^44 = 1 w^45 = sqrt(-1) If w = sqrt(-1) Then w^2 = -1 w^3 = -sqrt(-1) w^4 = (+)1 Hence any multiple of '4' in the index is equal to '1' w^44 + w^45 = 1 + sqrt(-1) w^44(1 + w) = 1 + sqrt(-1)