Question

If $\omega$ is a non real cube root of unity, then the expression $(1-\omega )(1-{\omega }^2)(1+{\omega }^4)(1+{\omega }^8)$ is equal to

• A. 0
• B. 3
• C. 1
• D. 2

Answer 1

Answer: (B)

3

$w^4=w^3.w$
$=w$
And
$w^8=w^6.w^2$
$=w^2$
Hence the overall expression becomes
$(1-w)(1-w^2)(1+w)(1+w^2)$
$=(1-w^2)(1-w^4)$
$=(1-w^2)(1-w)$
$=1-(w^2+w)+w^3$
$=1-(-1)+1$
$=3$