Question

If $Re{z}^2=0$ then the locus of z is

• A. Circle
• B. Parabola
• C. Pair of non-perpendicular lines
• D. Pair of perpendicular lines

Answer 1

The correct option is D Pair of perpendicular lines

Let,
$z=x+iy$
$z^2=x^2+2ixy-y^2$
$Re\left(z^2\right)=0$
$\Rightarrow x^2-y^2=0$
$\Rightarrow (x+y)(x-y)=0$
$\Rightarrow x+y=0orx-y=0$
Hence, option D is correct