If `z` is a complex number satisfying `z^4+z^3+2z^2+z+1=0` then the set of possible values of `z` is

Answer

1

Explanation

`z^(4)+ z^(3)+z^(2) + z+1=0`
`or (z^(2)(z^(2) +z+1)+(z^(2)+ z+1)) =0`
` or (z^(2) + z +1)(z^(2) + 1) =0`
`therefore z = i,-i, omega, omega^(2)`. For each `|z|= 1`