Question

If 1, $\omega ,{\omega }^2$ are the three cube roots of unity, then $(1+\omega {)}^3-(1+{\omega }^2{)}^3=0.$

• A. True
• B. False

Answer 1

The correct option is A True

$1+\omega +{\omega }^2=0$

$1+\omega =-{\omega }^2$ and $1+{\omega }^2=-\omega$

$(1+\omega {)}^3-(1+{\omega }^2{)}^3$

$⟹(-{\omega }^2{)}^3-(-\omega {)}^3$

$⟹-(\omega {)}^6+(\omega {)}^3$

$⟹-1+1=0$