primitive 5th root of unity extension

[mrbohn1]

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.

[morphism]

Hint: If |z|<1, do you know of another way of writing 1/(1-z)?

[mrbohn1]

aaah...I see - thanks. I wasn't expecting to have to use analysis in a galois theory exercise...