The equation of any in the complex plane is of the form (z z +b z + b z+c=0 ) where ((b C , c R ) )

Step-by-step solution

Let Equation of circle in cartesian system be (x^2+y^2+2 g x+2 f y+c=0 ) ...(i) ( aligned Let z & =x+i y z & =x-i y z+ z & =2 x z- z & =2 i y 2 y & = z- z i =i( z -z) z z & =(x+i y)(x-i y) z z & =x^2+y^2 aligned ) ( ) From Eq. (i) ( aligned z z +g(z+ z )+i( Z -Z) f+c & =0 z z +(g-i f) z+(g+i f) z +c & =0 z z + b z+b z +c & =0 [Let b=g+ if] aligned ) Hence, option (a) is correct.