Question

If $\omega$ is an imaginary cube root of unity, then $(1+\omega -{\omega }^2{)}^2$ equals

• A. $\omega$
• B. $-4\omega$
• C. ${\omega }^2$
• D. $4\omega$

Answer 1

The correct option is D $4\omega$

The value of $(1+\omega -{\omega }^2{)}^2=(-{\omega }^2-{\omega }^2{)}^2,$ since $1+\omega +{\omega }^2=0$
$=4{\omega }^4=4\omega ,$ since ${\omega }^3=1$