If 1, w, w2 are cube roots of unity, prove the following (1 - w + w2) (1+ w - - Maths - Determinants

Question

If 1, w, w2 are cube roots of unity, prove the following (1 - w +
w2) (1+ w - w2) = 4 do not give link solve it

Shruti Malhotra · Accepted Answer

Dear student

We know that w3=1 and 1+w+w2=0
Now,

1-w+w21+w-w2=1+w2-w1+w-w2=-w-w-w2-w2=-2w-2w2=4w3=4

If 1, w, w2 are cube roots of unity, prove the following (1 - w + w2) (1+ w - w2) = 4 do not give link solve it