Question

If $n$ is a positive integer not a multiple of $3$, then $1+{\omega }^n+{\omega }^{2n}=$

• A. $3$
• B. $1$
• C. $0$
• D. None of these

Answer 1

Answer: (C)

$0$

$1+{\omega }^n+{\omega }^{2n}$

If $n$ is not a multiple of $3$

$1+{\omega }^n+{\omega }^{2n}=0$

$\because {\omega }^3=1$

and according to cube-root unity.

$1+{\omega }^2+\omega =0$