The area of the polygon, whose vertices are the non-real roots of the equation z ¯ = i z 2 is

Step-by-step solution

z ¯ = i z 2 ⇒ x - i y = i x + i y 2 ⇒   x - i y = x 2 - y 2 i - 2 x y i.e., x = - 2 x y and - y = x 2 - y 2 ⇒   x = 0 , y = - 1 2 When x = 0 ; y = 0 , 1 When y = - 1 2 ; x = ± 3 2 0 , 0 will be rejected as vertices would be non-real roots. So, the vertices will be 0 , 1 ,   3 2 , - 1 2 and - 3 2 , - - 1 2 Hence, area of ∆ = 1 2 × 3 × 3 2 = 3 3 4