Question

Let $1,\omega ,{\omega }^2$ be the cube roots of unity , then the value of $(1-\omega )(1-{\omega }^2)(1-{\omega }^4)(1-{\omega }^5)=$

• A. $5$
• B. $7$
• C. $9$
• D. $11$

Answer 1

The correct option is C $9$

$(1-w)(1-w^2)(1-w^4)(1-w^5)$
$=(1-w)(1-w^2)(1-w^3.w)(1-w^3.w^2)$
Since $w^3=1$, the above equation transforms to
$=(1-w)(1-w^2)(1-w)(1-w^2)$
$=\left[\right(1-w\left)\right(1-w^2){]}^2$
$=(1-(w+w^2)+w^3{)}^2$
$=(1-(-1)+1{)}^2$
$=(3{)}^2$
$=9$