If $\omega$ is a complex cube root of unity, then $225 + \left( 3\omega + 8\omega^{2} \right)^{2} + \left( 3\omega^{2} + 8\omega \right)^{2}$ is equal to

Question

Dr. Abubacker · Accepted Answer

(d)
We have, $225 + \left( 3\omega + 8\omega^{2} \right)^{2} + \left( 3\omega^{2} + 8\omega \right)^{2}$
$= 225 + 9\omega^{2} + 64\omega^{4} + 48\omega^{3} + 9\omega^{4} + 64\omega^{2} + 48\omega^{3}$
$= 225 + 9\omega^{2} + 64\omega + 48 + 9\omega + 64\omega^{2} + 48$
$= 225 + 73\left( \omega^{2} + \omega \right) + 96 = 225 - 73 + 96 = 248$

Q. If $\omega$ is a complex cube root of unity, then $225 + \left( 3\omega + 8\omega^{2} \right)^{2} + \left( 3\omega^{2} + 8\omega \right)^{2}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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