If $Z \neq 0$ is a complex number such that $Z^2+Z|Z|+|Z|^2=0$ then $Z$ is in the set (Here $\omega$ is a complex cube root of unity)

• A

  $\{1\}$
• B

  $\{i,-i\}$
• Correct answer
  C

  $\left\{\omega, \omega^2\right\}$
• D

  $\phi$

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