VITEEE 2017 Paper

Consider the equation
z

−

z

+ (2 - 3i) z + (2 + 3i)

−

z

+ 4 = 0 ... (1)
Let z = x + iy and

−

z

= x - iy , z

−

z

= x2+y2
Put value of z,

−

z

and z

−

z

in equation (1),
we get
(x2+y2) + (2 - 3i) (x + iy) + (2 + 3i) (x - iy) + 4 = 0
⇒ 4x + 6y + 4 + x2+y2 = 0
Now, we make it perfect square
⇒ x2+y2 + 4x + 6y + 4 + 4 + 9 = 4 + 9
⇒ (x+2)2 + (y+3)2 = 9
This represents a circle of radius 3.