Question

The curve represented by $Im(z{)}^2=c(c\ne 0)$ is

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

Answer 1

The correct option is D a rectangular hyperbola

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