If (1) is a cube root of unity, and (1+)^7=A+B, then (A,B) equals

Question

If $\omega(
e1)$ is a cube root of unity, and $(1+\omega)^7=A+B\omega$, then $(A,B)$ equals

Accepted Answer

$${\left( {1 + \omega } \right)^7} = A + B\omega ;\,\,\,\,{\left( { - {\omega ^2}} \right)^7} = A + B\omega $$

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

$$ \Rightarrow A = 1,B = 1.$$

Solutions · 1