Answer to Question #74866 in Abstract Algebra for Rajni

Question #74866
Find the sum of the 5th roots of unity?
1
Expert's answer
2018-03-27T09:59:08-0400
We know that sum of roots of a n-degree polynomial is given by the negative of coefficient of x^(n-1) divided by coefficient of x^n.
So, x^5 – 1 is the polynomial whose roots are fifth roots of unity. Their sum is clearly zero because coefficient of x^4 is zero.

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