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 

$\alpha ,\beta ,\gamma ,\delta$ are the roots of the equation

$x^4+x^3+x^2+x+1=0$

Which are 5^th roots of unity except 1.

${\alpha }^5=1,{\beta }^5=1,{\gamma }^5=1,{\delta }^5=1,\alpha +\beta +\gamma +\delta =-1$,

then ${\alpha }^{2021}+{\beta }^{2021}+{\gamma }^{2021}+{\delta }^{2021}=\alpha +\beta +\gamma +\delta =-1$