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Arithmetic

Identities

Medium

If $1, \omega, \omega^2$ are the cube roots of unity, then the value of $\dfrac{1+9+11\omega^2}{\omega^2+9+11\omega} + \dfrac{3+5\omega+7\omega^2}{3\omega+5\omega^2+7}$ is:

$-1$

$\omega^2$

$\omega$

$0$

✅ Correct Option: 1

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If 1,ω,ω21, \omega, \omega^21,ω,ω2 are the cube roots of unity, then the value of 1+9+11ω2ω2+9+11ω+3+5ω+7ω23ω+5ω2+7\dfrac{1+9+11\omega^2}{\omega^2+9+11\omega} + \dfrac{3+5\omega+7\omega^2}{3\omega+5\omega^2+7}ω2+9+11ω1+9+11ω2​+3ω+5ω2+73+5ω+7ω2​ is: