The given expression is a product of linear terms of the roots of unity. We know that the sum of roots of unity is zero. Therefore, the product of (9 - ω) for all roots of unity is the same as the product of 9 for all roots of unity, because subtracting the roots of unity does not change the product.

The product of 9 for all roots of unity is 9^n, where n is the number of roots of unity. Therefore, the value of (9−ω)⋅(9−ω2)⋅(9−ω3)...(9−ωn−1) is 9^n.

Question

The given expression is a product of linear terms of the roots of unity. We know that the sum of roots of unity is zero. Therefore, the product of (9 - ω) for all roots of unity is the same as the product of 9 for all roots of unity, because subtracting the roots of unity does not change the product.

The product of 9 for all roots of unity is 9^n, where n is the number of roots of unity. Therefore, the value of (9−ω)⋅(9−ω2)⋅(9−ω3)...(9−ωn−1) is 9^n.

Knowee AI · Accepted Answer

The given expression is a product of linear terms of the roots of unity. We know that the sum of roots of unity is zero. Therefore, the product of (9 - ω) for all roots of unity is the same as the product of 9 for all roots of unity, because subtracting the roots of unity does not change the product.

The product of 9 for all roots of unity is 9^n, where n is the number of roots of unity. Therefore, the value of (9−ω)⋅(9−ω2)⋅(9−ω3)...(9−ωn−1) is 9^n.

If 1,ω,ω2,....ωn−1 are n,nth roots of unity, then the value of(9−ω)⋅(9−ω2)⋅(9−ω3)...(9−ωn−1) will be

Question

If 1, ω, ω², ....ωⁿ⁻¹ are n, nth roots of unity, then the value of (9−ω)⋅(9−ω²)⋅(9−ω³)...(9−ωn−1) will be

Solution

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