Question

If $z=x+iy$ and $Re\left(z^2\right)=0$, then the locus of $z$ can be

• A. $y=x$
• B. $y=-x$
• C. $y=2x$
• D. $y=-2x$

Answer 1

Answer: (A), (B)

The correct options are
A $y=x$
B $y=-x$

$z=x+iy\Rightarrow z^2=x^2-y^2+2ixy$
Now,
$Re\left(z^2\right)=0\Rightarrow x^2-y^2=0\Rightarrow y=x\text{or}y=-x$

Hence, the required locus are $y=x$ or $y=-x$