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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.

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# Primitive 5th root of unity extension

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