Answer to Question #74866 in Abstract Algebra for Rajni

Question

Find the sum of the 5th roots of unity?

Answer 1

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.