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:z⁴ + z³ + z² + z + 1 = 0.These roots can be represented in the form ?, ?², ?³, ?⁴ where ? = exp (2i/5). Let these correspond to the points P₁, P₂, P₃, P₄. Letting
:p₁ = ? + ?⁴, p₂ = ?² + ?³we have
:p₁ + p₂ = −1, p₁p₂ = -1.

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