Question

If $z=x+iy$ and if the point $P$ in the Argand plane represents $z$, then describe geometrically the locus of $z$, satisfying the equation on
$Img{z}^2=4$

Answer 1

$z^2=(x+iy{)}^2=x^2-y^2+2ixy$

$\Rightarrow Re\left(z^2\right)=x^2-y^2=4$

$\Rightarrow \frac{x^2}{4}-\frac{y^2}{4}=1$ of form $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

$\Rightarrow$ It is a hyperbola.