Question

Geometrically $Re(z^2-i)=2$, where $i=\sqrt{-1}$ and $Re$ is the real part, represents.

• A. circle
• B. ellipse
• C. rectangular hyperbola
• D. parabola

Answer 1

Answer: (C)

rectangular hyperbola

Let $z=x+iy$

$\therefore Re\left(\right(x+iy{)}^2-i)=2⟹Re(x^2-y^2+i(2xy-1))=2⟹x^2-y^2=2⟹\frac{x^2}{2}-\frac{y^2}{2}=1$

This is the generalised form of a hyperbola and as minor axis and major axis are same for the hyperbola, it is a rectangular hyperbola.