Question

cube roots of unity

Answer 1

$Cube \: roots \: of \: unity \: are \: 1, w, and \: {w}^{2}. \\ {w}^{13} = {w}^{1} \\ and \: {w}^{17} = {w}^{2}$
By expanding, you get,
$(4 - {w}^{4} )(4 - {w}^{2} ) \\ = (4 - w)(4 - {w}^{2} ) \\ = 16 - 4(w + {w}^{2} ) + 1 \\ = 17 - 4( - 1) \\ = 21$