Question

If $Z$ is a non zero complex number such that $Re\left(Z\right)=0,$ then

• A. $Re\left(Z^2\right)=0$
• B. $Im\left(Z^2\right)\ne 0$
• C. $Im\left(Z^2\right)=0$
• D. $Re\left(Z^2\right)+Im\left(Z^2\right)=0$

Answer 1

The correct option is C $Im\left(Z^2\right)=0$

Let $Z=x+iy$
As $Re\left(Z\right)=0$, so $Z=iy$
Now,
$Z^2=(iy{)}^2=-y^2$
As $Z$ is non zero complex number, so $y\ne 0$
Therefore,
$Im\left(Z^2\right)=0$