Question

If $\omega$ being the cube root of unity then find the value of $(1-\omega +{\omega }^2)(1+\omega -{\omega }^2)$.

Answer 1

Given $\omega$ being the cube root of unity.

Now,

$(1-\omega +{\omega }^2)(1+\omega -{\omega }^2)$

$=(-2\omega )(-2{\omega }^2)$

[Since $1+\omega +{\omega }^2=0$ and ${\omega }^3=1$]

$=4{\omega }^3$

$=4$.