If $\alpha$ and $\beta$ are the complex cube roots of unity, then what is the value of $(1+\alpha)(1+\beta)\left(1+\alpha^2\right)\left(1+\beta^2\right)$ ?

• A

  $-1$
• B

  $0$
• Correct answer
  C

  $1$
• D

  $4$

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