Q. If $\alpha$ is a cube root of unit and is not real, then $\alpha^{3n + 1} + \alpha^{3n + 3} + \alpha^{3n + 5}$ has the value
A) $- 1$
B) 0
C) 1
D) 3
Explanation
(b)
Since, $\alpha$ is an imaginary cube root of unity. Let it be $\omega$, then $\alpha^{3n + 1} + \alpha^{3n + 3} + \alpha^{3n + 5} = (\omega)^{3n + 1} + (\omega)^{3n + 3} + (\omega)^{3n + 5}$
$= \omega + 1 + \omega^{5}$
$= \ \omega + 1 + \omega^{2} = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.