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)/(2) " " rArr ( xy - (x- 2) (y + 1))/(x^(2) + (y+1)) = (1)/(2)`
`rArr " " 2 (-x + 2y + 2) = x^(2) + y^(2) + 2y + 1 " " rArr " " x^(2)+ y^(2) - 2y + 2x - 3 = 0 ` Cirle.