If $z=x+i y$ and $z^2=(i \bar{z})^2$, then

• A

  $y= \pm \frac{x}{\sqrt{3}}$
• Correct answer
  B

  $y= \pm x$
• C

  $y= \pm \frac{x}{2}$
• D

  $x=0, y= \pm 1$

Hence, the correct answer is option: 'B'.