Question

If $\omega$ is the cube root of unity then $(1-\omega +{\omega }^2{)}^6=$

• A. $0$
• B. $1$
• C. $64$
• D. $32$

Answer 1

The correct option is C $64$

Given $\omega$ being cube root of unity.

Then,

$(1-\omega +{\omega }^2{)}^6$

$=(-2\omega {)}^6$ [Since $1+{\omega }^2=-\omega$]

$=64$ [Since ${\omega }^3=1\Rightarrow {\omega }^6=1$]