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Grade: 12

                        

If 1, w, w2 are cube roots of unity, prove the following:(1 - w + w^2) (1+ w - w^2) = 4

If 1, w, w2 are cube roots of unity, prove the following:(1 - w + w^2) (1+ w - w^2) = 4

2 months ago

Answers : (1)

Anand Kumar Pandey
askIITians Faculty
4371 Points
							Dear Student

1+ w + w^2 = 0
so 1 + w = – w^2
1+ w^2 = – w
(1 - w + w^2)= –2w
(1+ w - w^2)= –2w^2
(1 - w + w^2) (1+ w - w^2)= (-2w)( –2w^2)
= 4w^3
and we know that w^3=1
Hence, proved

Thanks
2 months ago
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