\sqrt[5]{1} = -\frac{1}{4} \quad+\frac{1}{4}\cdot\sqrt{5}\quad+\frac{1}{2}\cdot\sqrt{-\frac{5}{2}-\frac{1}{2}\cdot\sqrt{5}} Ripped out of Constructing Regular Polygons -- Primitive Roots of Unity.
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\sqrt[5]{1} = -\frac{1}{4} \quad+\frac{1}{4}\cdot\sqrt{5}\quad+\frac{1}{2}\cdot\sqrt{-\frac{5}{2}-\frac{1}{2}\cdot\sqrt{5}} 
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