Question

If $\omega$ is complex cube root of unity , then $(1-\omega +{\omega }^2{)}^6+(1-{\omega }^2+\omega {)}^6=$

• A. 0
• B. 6
• C. 64
• D. 128

Answer 1

Answer: (D)

128

We have,

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

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

Hence, the given expression is same as

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

$=64{\omega }^6+64{\omega }^{12}$

$=64+64$

$=128$