The number of solutions of the equation z 3 + 3 z ¯ 2 z = 0 (where, z is a complex number) are

Step-by-step solution

Let, z = r e i θ ⇒ r 3 e i 3 θ + 3 r e - i 2 θ = 0 ⇒ r 2 e i 5 θ = - 3 ⇒ r 2 = 3 and e i 5 θ = - 1 ⇒ r = 3 and θ = π 5 + 2 k 5 where, k = 0 , 1 , 2 , 3 , 4 ⇒ 5 solutions