Question

If $\omega$ is non-real cube root of unity then ${(1+\omega -{\omega }^2)}^7$ equal

• A. $-128{\omega }^2$
• B. $128{\omega }^2$
• C. $-128\omega$
• D. $128\omega$

Answer 1

The correct option is A $-128{\omega }^2$

Since $w$ is the cube root of unity.
$\therefore w^3=1\&1+w+w^2=0$
$z={(1+w-w^2)}^7={(-w^2-w^2)}^7=-2^7{w}^{14}=-128{\left(w^3\right)}^4{w}^2\therefore z=-128w^2$
Ans: A