If the complex number ω = x + i y ( ∀ x , y ∈ R and i 2 = - 1 ) satisfy the equation ω 3 = 8 i , then the maximum value of y is

Step-by-step solution

ω = 2 ⋅ i 1 3 = 2 cos ⁡ 2 nπ + π 2 + i sin ⁡ 2 n π + π 2 1 3 = 2 cos ⁡ 2 n π + π 2 3 + i sin ⁡ 2 n π + π 2 3 Put n = 1 = 2 cos ⁡ 5 π 6 + i sin ⁡ 5 π 6 = - 3 + i Hence, the maximum value of y is 1