Question

If $\omega$ is a cube root of unity, then $(1+\omega -{\omega }^2)(1-\omega +{\omega }^2)$ =
[MNR 1990; MP PET 1993, 2002]

• A. 1
• B. 0
• C. 2
• D. 4

Answer 1

The correct option is D 4

If $\omega$ is a complex cube root of unity then ${\omega }^3=1$ and $1+\omega +{\omega }^2=0,$ therefore $(1+\omega -{\omega }^2)(1-\omega +{\omega }^2)$
$=(-2{\omega }^2)(-2\omega )=4$