Question

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

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

Answer 1

The correct option is A Rectangular hyperbola

Let
$z=x+iy$
$z^2=(x^2-y^2)+i\left(2xy\right)$
Now
$Im\left(z^2\right)$
$=2xy$
$=\lambda$
Hence
$2xy=\lambda$
$xy=\frac{\lambda }{2}$
This represents a rectangular hyperbola of type $xy=c$ where c is a constant.