Question

If $\omega$ is an imaginary cube root of unity, then (1 + $\omega$ - $\omega^2)^7$ is equal to

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

Answer 1

Answer: (D)

-128$\omega^2$

Answer 2

$(1+\omega-\omega^2)^7=(-\omega^2-\omega^2)^7 \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, [\because 1+\omega+\omega^2=0]$
$=(-2\omega^2)^7=(-2)^7\omega^{14}=-128 \omega^2$