Two points P and Q in the argand plane represent the complex numbers z and 3 z + 2 + i . If z = 2 , then Q moves on the circle, whose centre and radius are (here, i 2 = - 1 )

Step-by-step solution

z = 2 x 2 + y 2 = 4 3 x + i y + 2 + i = h + i k 3 x + 2 + i 3 y + 1 = h + i k h = 3 x + 2 , k = 3 y + 1 h - 2 3 = x , k - 1 3 = 4 h - 2 3 2 + k - 1 3 2 = 4 ⇒ h 2 + 4 - 4 h + k 2 + 1 - 2 k = 36 ⇒ h 2 + k 2 - 4 h - 2 k - 31 = 0 Centre = 2,1 Radius = 4 + 1 + 31 = 6