Question

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

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

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. $=4^n$