Question

Let $\omega$ be cube root of unity then the expression $(1+\omega )(1+{\omega }^2)(1+{\omega }^4)(1+{\omega }^8)...$upto $2n$ terms is equal

• A. 0
• B. 1
• C. 3
• D. -1

Answer 1

Answer: (B)

1

Given,

$(1+w)(1+w^2)(1+w^4)(1+w^8)$ upto 2n terms

considering first 2 terms, we get,

$(1+w)(1+w^2)=1+w^2+w+w^3=0+w^3=1$

similarly, considering second 2 terms, we get,

$(1+w^4)(1+w^8)=(1+w)(1+w^2)=1$

It continues for all the remaining pair of terms,

therefore the product upto 2n terms equals 1.

hence B is correct answer