40. O -7 points SPreCalc7 8.3 100 ) + ? where n is a positive integer. It can be

Question

40. O -7 points SPreCalc7 8.3 100 ) + ? where n is a positive integer. It can be shown that the n distinct roots of 1 are Let w-cos sin 1, w, w, w.w Find the product of the three cube roots of 1. Find the product of the four fourth roots of 1 Find the product of the five fifth roots of 1. Find the product of the six sixth roots of 1. Find the product of the eight eighth roots of 1. What do you think is the product of the nth roots of 1 for any n? The product of the n roots of unity is if o is even and if n is odd. Need Help? Read a Show My Work optoat

Explanation / Answer

Product of nth roots of unity is either (1 - odd) or (-1 even)

(1)

Product of the three cube roots of unity = 1

(2)

-1

(3)

1

(4)

-1

(5)

1

The product of roots of unity is -1 if n is even and 1 if n is odd

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