The number of distinct complex number(s) z , such that z = 1 and z 3 is purely imaginary, is/are equal to

Step-by-step solution

Let, z = e i θ ⇒ z 3 = cos ⁡ 3 θ + i sin ⁡ 3 θ Since, z 3 is purely imaginary ⇒ cos ⁡ 3 θ = 0 ⇒ θ = 2 n π 3 ± π 6 ∴ Possible value of θ = 30 o , 150 o , 90 o , 270 o , 210 o , 330 o .