Question

If $\omega$ is a non real cube root of unity and n is a positive integer which is not a multiple of 3, then $1+{\omega }^n+{\omega }^{2n}$ is equal to

• A. 3$\omega$
• B. 0
• C. 3
• D. none of these

Answer 1

The correct option is B 0

$\omega$ is a non real cube root of unity and $n$ is a positive integer which is not a multiple of $3$.
i.e one of ${\omega }^n$ and ${\omega }^{2n}$ is $\omega$ and other one is ${\omega }^2$
$\Rightarrow 1+{\omega }^n+{\omega }^{2n}=0$
Hence, option B.