Question

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

• (A) 2
• (B) 3
• (C) 5
• (D) 6

Answer 1

The Correct Option is B

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