The solutions to the equation zⁿ = 1 for n = 1, 2, 3, 4, 5 and 6 all lie on the unit circles shown. They are designated complex unit roots of degree n. The number 1 (marked with a green dot) is a trivial solution in all cases. The complex numbers ε₂ = –1, ε₃ = –1/2 + √3/2·i, ε₄ = i, ε₅ = (√5 – 1)/4  + √(10 + 2√ 5)/4·i and  ε₆ = √3/2+ 1/2·i  are identified by red dots. They and their powers (marked with black dots) are the complex unit roots of degrees between 2 and 6.
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AstroOgier