Question

If $\omega$ is an imaginary cube root of unity then $(1+\omega -{\omega }^2{)}^7$ equals?

• A. $128\omega$
• B. $-128\omega$
• C. $-128{\omega }^2$
• D. None of these

Answer 1

The correct option is C $-128{\omega }^2$

Q. If $\omega$ is an imaginary. cube root of unity

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

Sol${}^n$ as we know $1+\omega +{\omega }^2=0\&{\omega }^3=1$

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

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

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

$=(-2{)}^7.{\omega }^{14}.(1)$

$=-128.{\omega }^{14}.{\omega }^3$

$=-128.{\omega }^{17}$

$=-128.({\omega }^3{)}^5.{\omega }^2$

$(1+\omega -{\omega }^2{)}^7=-128{\omega }^2$