Question

If $\alpha$ and $\beta$ are imaginary cube roots of unity, then $\alpha^4+\beta^4+\frac{1}{\alpha \beta}$ is equal to

(A) 3

(B) 0

(C) 1

(D) 2

Answer 1

Since, $\alpha$ and $\beta$ are the imaginary cube roots of unity.

Let

$\therefore \quad \alpha^4+\beta^4+\frac{1}{\alpha \beta}$

$=\omega^4+\left(\omega^2\right)^4+\frac{1}{\omega \omega^2}$

$=\omega+\omega^2+1=0 \quad\left[\because \omega^3=1\right]$

So, The correct option will be (B).