Question

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

• A. 2
• B. 3
• C. 5
• D. 6

Answer 1

Answer: (B)

Given, $(1+{\omega }^2{)}^n=(1+{\omega }^4{)}^n$
$\Rightarrow (-\omega {)}^n=(-{\omega }^2{)}^n[\because w^3=1$ and $1+\omega +{\omega }^2=0]$
$\Rightarrow {\omega }^n=1$
$\Rightarrow n=3$ is the least positive value of $n$.