If ` z = x + iy, x , y in R ` , then the louts `Im (( z - 2 ) /(z + i)) = (1 ) /(2) ` represents : ( where ` i= sqrt ( - 1)) `

Options

A. Straight line
B. Circle
C. Parabola
D. Hyperbola

Answer

B

Explanation

`Im((z-2)/(z+i))=1/2 rArr Im[((x-2)+iy)/(x+(y+1)i)]=1/2`
`rArr Im[({(x-2)+iy}{x-i(y+1)})/(x^2+(y+1)^2)]=1/2rArr (xy-(x-2)(y+1))/(x^2+(y+1)^2)=1/2`
`rArr 2(-x+2y+2)=x^2+y^2+2y+1 rArr x^2+y^2-2y+2x-3=0` Circle