Question

The value of $\left(1-\omega+\omega^2\right)\left(1-\omega^2+\omega^4\right)\left(1-\omega^4+\omega^8\right) \ldots \ldots \ldots$. to $2 n$ factors is

• A. $2^n$
• B. $4^n$
• C. $4 n$
• D. $2 n$

Answer 1

Answer: (B)

$\left(1-\omega+\omega^2\right)\left(1+\omega^4-\omega^2\right)=(-2 \omega)\left(-2 \omega^2\right)=4$
similarly total we have and terms and each equal to 4
$\therefore $ Ans. $=4^n$