八十四角形
2 cos  2 π 84 + 2 cos  74 π 84 + 2 cos  50 π 84 = 3 − 7 2 = x 1 2 cos  38 π 84 + 2 cos  62 π 84 + 2 cos  58 π 84 = − 3 − 7 2 = x 2 2 cos  34 π 84 + 2 cos  82 π 84 + 2 cos  10 π 84 = − 3 + 7 2 = x 3 2 cos  26 π 84 + 2 cos  46 π 84 + 2 cos  22 π 84 = 3 + 7 2 = x 4 {\displaystyle {\begin{aligned}2\cos {\frac {2\pi }{84}}+2\cos {\frac {74\pi }{84}}+2\cos {\frac {50\pi }{84}}={\frac {{\sqrt {3}}-{\sqrt {7}}}{2}}=x_{1}\\2\cos {\frac {38\pi }{84}}+2\cos {\frac {62\pi }{84}}+2\cos {\frac {58\pi }{84}}={\frac {-{\sqrt {3}}-{\sqrt {7}}}{2}}=x_{2}\\2\cos {\frac {34\pi }{84}}+2\cos {\frac {82\pi }{84}}+2\cos {\frac {10\pi }{84}}={\frac {-{\sqrt {3}}+{\sqrt {7}}}{2}}=x_{3}\\2\cos {\frac {26\pi }{84}}+2\cos {\frac {46\pi }{84}}+2\cos {\frac {22\pi }{84}}={\frac {{\sqrt {3}}+{\sqrt {7}}}{2}}=x_{4}\\\end{aligned}}}
2 cos  2 π 84 + ω ⋅ 2 cos  74 π 84 + ω 2 ⋅ 2 cos  50 π 84 = 11 3 + 9 7 − 3 3 ( 7 3 + 5 7 ) i 4 3 2 cos  2 π 84 + ω 2 ⋅ 2 cos  74 π 84 + ω ⋅ 2 cos  50 π 84 = 11 3 + 9 7 + 3 3 ( 7 3 + 5 7 ) i 4 3 {\displaystyle {\begin{aligned}2\cos {\frac {2\pi }{84}}+\omega \cdot 2\cos {\frac {74\pi }{84}}+\omega ^{2}\cdot 2\cos {\frac {50\pi }{84}}=&{\sqrt[{3}]{\frac {11{\sqrt {3}}+9{\sqrt {7}}-3{\sqrt {3}}(7{\sqrt {3}}+5{\sqrt {7}})i}{4}}}\\2\cos {\frac {2\pi }{84}}+\omega ^{2}\cdot 2\cos {\frac {74\pi }{84}}+\omega \cdot 2\cos {\frac {50\pi }{84}}=&{\sqrt[{3}]{\frac {11{\sqrt {3}}+9{\sqrt {7}}+3{\sqrt {3}}(7{\sqrt {3}}+5{\sqrt {7}})i}{4}}}\\\end{aligned}}}