Question

If ω is a complex cube root of unity and ${(1+\omega )}^7$ = A + B$\omega$ , then (A, B) is

• A. 0,1
• B. 1,0
• C. 1,1
• D. -1,-1

Answer 1

The correct option is C

1,1

We know the relation 1 + $\omega$ + ${\omega }^2$ = 0
1 + $\omega$ = - ${\omega }^2$
${(1+\omega )}^7$ = ${(-{\omega }^2)}^7$ = - ${\left(\omega \right)}^{14}$
= - ${\omega }^{12}$${\omega }^2$
= - ${\left({\omega }^3\right)}^4$ ${\omega }^2$
= - ${\omega }^2$

1 + $\omega$ = -${\omega }^2$
A + B$\omega$ = 1 + $\omega$
A = 1 , B = 1