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Q.
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
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 $n$.