$\omega$ is a complex cube root of unity and Z is a complex number satisfying $|\mathrm{Z}-1| \leq 2$. The possible values of $r$ such that $|\mathrm{Z}-1| \leq 2$ and $\left|\omega \mathrm{Z}-1-\omega^2\right|=r$ have no common solution are

• A

  $0 \leq r \leq 4$
• B

  $r=|\omega|$ only
• Correct answer
  C

  $r>4$
• D

  $1 < r < 2$

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