If $1,\ \omega,\omega^{2}$ are the cube roots of unity, then $\omega^{2}(1 + \omega)^{3} - (1 + \omega^{2})\omega$ is equal to

Question

Dr. Abubacker · Accepted Answer

(d)
$\omega^{2}(1 + \omega)^{3} - (1 + \omega^{2})\omega$
$= \omega^{2}\left( - \omega^{2} \right)^{3} - ( - \omega)\omega\ \ \ \ \ \ \ \lbrack\because\ \ 1 + \omega + \omega^{2} = 0\rbrack$
$= - \omega^{2}\left( \omega^{3} \right)^{2} + \omega^{2} = 0\ \ \ \ \ \ \ \ \lbrack\because\ \ \omega^{3} = 1\rbrack$

Q. If $1,\ \omega,\omega^{2}$ are the cube roots of unity, then $\omega^{2}(1 + \omega)^{3} - (1 + \omega^{2})\omega$ is equal to

Explanation

Reviewed by Dr. Abubacker

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