# U4 set

1. Jul 4, 2006

### Taviii

I saw this problem in a book: calculate the sum of the elements of the U4 set.

The answer is 0, the elements of the sets being: 1, i, -1, -i.

My questions is: whats the U set?

Last edited: Jul 4, 2006
2. Jul 4, 2006

### maverick280857

In this terminology $U_{n}$ refers to the set of the n-th roots of unity, i.e. all roots of the equation

$$x^{n} - 1 = 0$$

So

$U_{3}$ = {1, $\omega$,$\omega^2$}

3. Jul 5, 2006

### Taviii

Thank you!

Your explanation was very helpful.

4. Jul 6, 2006

### HallsofIvy

If you multiply out (x-a1)(x-a2)...(x-an) the coefficient of x is easily seen to be -(a1+ a2+ ...+ an) so for any polynomial equation in which there is no "x" term, the sum of the roots must be 0. In particular, the sum of the roots of xn= 1 must be 0 for all n and so the sum of the elements of Un must be 0 for all n.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook