Question

If 1 , w, w are cube roots of unity, then prove the following

Answer 1

If 1, w, w2 are the cube roots of unity, then the value of (1 + w2 - w) (1 - w2 + w) is?

As 1+w+w^2 is zero the given expression reduces to -2w×-2w^2 .As w^3 is equal to 1 the final value is 4.

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1, w, w^2 are cube roots of unity

Then, we know that 1+w+w^2=0

1+w = -w^2 and 1+w^2 = -w

Substitute it in the given expression

(1 + w^2 - w) (1 - w^2 + w)

(-w -w) (-w^2 -w^2)

(-2w) (-2w^2) = 4w^3

Since w^3 = 1

The answer is 4.

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