Question

If $\omega (\ne 1)$ is a cube root of unity and ${\left(1+{\omega }^2\right)}^n={\left(1+{\omega }^4\right)}^n$, then the least positive value of $n$ is

• A. 2
• B. 3
• C. 5
• D. 6

Answer 1

Answer: (B)

We have, ${\left(1+{\omega }^2\right)}^n={\left(1+{\omega }^4\right)}^n$
$\Rightarrow (-\omega {)}^n={\left(-{\omega }^2\right)}^n$
$\Rightarrow {\omega }^n=1$
$\Rightarrow n=3$ is least positive value of $n$.