Question

If $\omega$ is a cube root of unity, then $(2+5\omega +2{\omega }^2{)}^6=(2+2\omega +5{\omega }^2{)}^6=729$

• A. True
• B. False

Answer 1

The correct option is A True

$(2+\omega +5\omega +2{\omega }^2{)}^6$

$⟹(2+\omega +2\omega +2{\omega }^2+3\omega {)}^6$

$⟹(2\ast 0+3\omega {)}^6=3^6.w^6=729$

$(2+\omega +2\omega +5{\omega }^2{)}^6$

$⟹(2+\omega +2\omega +2{\omega }^2+3{\omega }^2{)}^6$

$⟹(2\ast 0+3{\omega }^6{)}^6=3^6.w^{12}=729$

Hence proved.