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U4 set

  1. Jul 4, 2006 #1
    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? :confused:
    Last edited: Jul 4, 2006
  2. jcsd
  3. Jul 4, 2006 #2
    In this terminology [itex]U_{n}[/itex] refers to the set of the n-th roots of unity, i.e. all roots of the equation

    [tex]x^{n} - 1 = 0[/tex]


    [itex]U_{3}[/itex] = {1, [itex]\omega[/itex],[itex]\omega^2[/itex]}
  4. Jul 5, 2006 #3
    Thank you!

    Your explanation was very helpful.
  5. Jul 6, 2006 #4


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    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.
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