Question

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

• A. ( 1,0 )
• B. ( -1,1 )
• C. ( 0,1 )
• D. ( 1,1 )

Answer 1

The correct option is D

( 1,1 )

$(1+\omega {)}^7$ = A + B$\omega$ $\Rightarrow$ 1 + $\omega$ = A + B $\omega$ $\Rightarrow$ (A.B) = (1, 1)