Question

Let $\omega$ being cube root of unity. Then the value of $(1+\omega -{\omega }^2{)}^7$ is

• A. $-2^7$
• B. $2^7$
• C. $-2^7{\omega }^3$
• D. $-2^7{\omega }^2$

Answer 1

Answer: (D)

$-2^7{\omega }^2$

Now,

$(1+\omega -{\omega }^2{)}^7$

$=(-{\omega }^2-{\omega }^2{)}^7$ [ Since $1+\omega +{\omega }^2=0$]

$=(-2{\omega }^2{)}^7$

$=-2^7{\omega }^2$ [ Since ${\omega }^{14}=({\omega }^3{)}^4.{\omega }^2={\omega }^2$] and $[{\omega }^3=1]$