Q57 / 90 · JEE Main 2011 · Mathematics

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

  • Correct answer
    A
    $(1,1)$
  • B
    $(1,0)$
  • C
    $(-1,1)$
  • D
    $(0,1)$

Solution

$1+\omega=-\omega^2$ $(1+\omega)^7=\left(-\omega^2\right)^7=-\omega^{14}=-\omega^2=1+\omega=A+B \omega \Rightarrow(A, B)=(1,1)$

Hence, the correct answer is option: 'A'.

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