Question

If $z=x+iy$ is a complex number, then the curve represented by $Im\left(z^2\right)=c^2$, where $c$ is non zero real constant, is a

• A. circle
• B. straight line
• C. ellipse
• D. rectangular hyperbola

Answer 1

The correct option is D rectangular hyperbola

Given : $z=x+iy$
Now,
$z^2=x^2-y^2+2ixy\Rightarrow Im(x^2-y^2+2xyi)=c^2\Rightarrow 2xy=c^2\Rightarrow xy=\frac{c^2}{2}$

Which is a equation of rectangular hyperbola.