Question

If $\omega$ is a non-real cube root of unity, then the value of ${(1-\omega +{\omega }^2)}^5+{(1+\omega -{\omega }^2)}^5$ is

• A. 16
• B. 32
• C. 48
• D. -32

Answer 1

The correct option is B 32

$(1-\omega +{\omega }^2{)}^5+(1+\omega -{\omega }^2{)}^5=(-\omega -\omega {)}^5+(-{\omega }^2-{\omega }^2{)}^5=-2^5{\omega }^5-2^5{\omega }^5-2^5({\omega }^5+{\omega }^{10})=-32({\omega }^2+\omega )=-32\cdot -1=32$