Question

The curve represented by $Im(z^2)=\lambda (\lambda \ne 1)$ is

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

Answer 1

Answer: (A)

Let $z=x+iy$
$\therefore z^2=(x^2-y^2)+2ixy$
$\therefore Im(z^2)=2xy$
$\Rightarrow 2xy=\lambda$
$\Rightarrow xy={\lambda }^{\prime }$
which is a rectangular hyperbola.