If \(1, \omega, \omega^2\) are the cube roots of unity, then the value of \( \dfrac{1+9\omega+11\omega^2}{\omega^2+9+11\omega} + \dfrac{3+5\omega+7\omega^2}{3\omega+5\omega^2+7} \) is:
Question and options
If are the cube roots of unity, then the value of is:
Answer and explanation
Correct answer: A - \(-1\)
Denominator w^2+9+11w = w^2(1+9w+11w^2) (using w^3=1, w^4=w), so first term = 1/w^2 = w. Similarly 3w+5w^2+7 = w(3+5w+7w^2), so second term = 1/w = w^2. Sum = w + w^2 = -1.
Practice for these exams
-
IIM Bangalore BBA DBE Entrance Test