Question

The equation $z^2+{\bar{z}}^2-2|z{|}^2+z+\bar{z}=0$ represents a

• A. straight line
• B. circle
• C. hyperbola
• D. parabola

Answer 1

Answer: (D)

We have, $z^2+{\bar{z}}^2-2|z{|}^2+z+\bar{z}=0$
$\Rightarrow (x+iy{)}^2+(x-iy{)}^2-2\left(x^2+y^2\right)+x+iy+x-iy=0$
$($ Putting $z=x+iy)$
$\Rightarrow 2x^2+2(iy{)}^2-2x^2-2y^2+2x=0$
$\Rightarrow -4y^2+2x=0$
or $y^2=\frac{1}{2}x$
which is a parabola.