Let $\omega$ be a complex root of the quadratic polynomial $x^2+x+1$. The value of
$\left(\omega+\frac{1}{\omega}\right) \cdot\left(\omega^2+\frac{1}{\omega^2}\right) \cdots\left(\omega^{100}+\frac{1}{\omega^{100}}\right)$ is

• A

  $-2^{31}$
• B

  $2^{33}$
• Correct answer
  C

  $-2^{33}$
• D

  $2^{31}$

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