[JEE Main 2011] If $\omega(\ne1)$ is a cube root of unity and $(1+\omega)^7=A+B\omega$, then $(A,B)$ equals
If $\omega(\ne1)$ is a cube root of unity and $(1+\omega)^7=A+B\omega$, then $(A,B)$ equals
(a) $(1,1)$
(b) $(1,0)$
(c) $(-1,1)$
(d) $(0,1)$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
▲ 0
Correct answer: (a) $(1,1)$
$1+\omega=-\omega^2$, so $(1+\omega)^7=-\omega^{14}=-\omega^2=1+\omega$. Hence $A+B\omega=1+\omega\Rightarrow(A,B)=(1,1)$.
JEE Main 2011 · Complex Numbers — verified solution by the Vidaara Team.
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