Question

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

• A. $0$
• B. $3$
• C. $1$
• D. $2$

Answer 1

Answer: (B)

$3$

$1+\omega +{\omega }^2=0$
${\omega }^3=1$
${\omega }^4=\omega$
${\omega }^8={\omega }^2$
$(1+{\omega }^4)=(1+\omega )=-{\omega }^2$
$(1+{\omega }^8)=(1+{\omega }^2)=-\omega$
put all values in given equation which comes out 3.