Topic: Electronics Engineering
$\alpha, \beta$ are the roots of the equation $x^{2}+x+1=0$ Then $\alpha^{3n}+\beta^{3n}$ is
- A. 1
- B. 2
- C. 0
- D. 3
Answer: B. 2
Explanation: $\alpha,\beta=\frac{-1\pm j\sqrt{3}}{2}$
So $\alpha$ and $\beta$ are cube roots of unity. $\alpha^{3}=\beta^{3}=1$
So, $(\alpha^{3})^{n}+(\beta^{3})^{n} = 1+1=2$