Let z 0 be a root of quadratic equation, x 2 + x + 1 = 0 . If z = 3 + 6 i z 0 81 - 3 i z 0 93 , then a r g z is equal to:

Step-by-step solution

z 0 = w or w 2 When z 0 = w z = 3 + 6 i × w 81 - 3 i × w 93 = 3 + 6 i - 3 i = 3 + 3 i When z 0 = w 2 z = 3 + 6 i × w 2 81 - 3 i × w 2 93 = 3 + 6 i - 3 i = 3 + 3 i ∴ arg ⁡ z = tan - 1 I m z R e z = tan - 1 ⁡ 3 3 = π 4