Question

$\alpha \beta$ equals

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is D $2$

Multiplying $\alpha \beta ={\omega }^4+{\omega }^6+{\omega }^7+{\omega }^5+{\omega }^7+{\omega }^8+{\omega }^7+{\omega }^9+{\omega }^{10}$
Now, ${\omega }^7=1,{\omega }^8=\omega ,...{\omega }^{10}={\omega }^3$ and $1+\omega +{\omega }^2+{\omega }^3+{\omega }^4+{\omega }^5+{\omega }^6=0$
Thus, $\alpha \beta ={\omega }^4+{\omega }^6+1+{\omega }^5+1+\omega +1+{\omega }^2+{\omega }^3=2$.