Question

If $\alpha$ and $\beta$ are the complex cube roots of unity,then ${\alpha }^4+{\beta }^2+{\alpha }^{-1}{\beta }^{-1}$ is equal to:

• A. 0
• B. 1
• C. -1
• D. None of these

Answer 1

The correct option is A 0

Since $\alpha ,\beta$ are the complex roots of unity

$\alpha =w;\beta =w^2$

Hence ${\alpha }^4+{\beta }^4+{\alpha }^{-1}{\beta }^{-1}=w^4+w^8+w^{-1}{w}^{-2}=w^3.w+w^6.w^2+w^{-3}(\because w^3=1)$

$=w+w^2+1=w^2+w+1=0$