Question

If z is complex number such that $z\ne 0$ and $R_e\left(z\right)=0$, then

• A. $Re\left(z^2\right)=0$
• B. $Im\left(z^2\right)=0$
• C. $Re\left(z^2\right)=Im\left(z^2\right)$
• D. none of these

Answer 1

The correct option is B $Im\left(z^2\right)=0$

$Re\left(z\right)=0$

$z=x+iy$

So

$z=iy$ as $x=0$

Now,

$z^2=(iy{)}^2=i^2{y}^2=-y^2$

So we can see that $z^2$ is free from imaginary term and hence

$Im\left(z^2\right)=0$