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Primitive 5th root of unity extension

  1. Aug 18, 2008 #1
    Hi,

    Let E = Q(a), where a is a primitive fifth root of unity. Find a basis for E as a vector space over Q, and express a/a-3 in terms of this basis.

    I can find a basis for E: {1, a, a^2, a^3}, but am not sure how to express a/a-3 in terms of this basis. Any help much appreciated.
     
  2. jcsd
  3. Aug 18, 2008 #2

    morphism

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    Hint: If |z|<1, do you know of another way of writing 1/(1-z)?
     
    Last edited: Aug 18, 2008
  4. Aug 19, 2008 #3
    aaah...I see - thanks. I wasn't expecting to have to use analysis in a galois theory exercise...
     
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