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Q.
If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x ^4+ x ^3+ x ^2+ x +1=0$, then $\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}$ is equal to .
JEE MainJEE Main 2022Complex Numbers and Quadratic Equations
Solution:
$\alpha, \beta, \gamma, \delta$ root of the equation
$x^4+x^3+x^2+x+1=0$
Which are $5^{\text {th }}$ roots of unity except 1 . then $\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}=$ $\alpha+\beta+\gamma+\delta=-1$