百八角形
2 cos  2 π 108 = cos  2 π 36 + i sin  2 π 36 3 + cos  2 π 36 − i sin  2 π 36 3 cos  2 π 108 = 3 + i 2 3 3 + 3 − i 2 3 3 2 = − i ω 3 3 + i ω 2 3 3 2 {\displaystyle {\begin{aligned}2\cos {\frac {2\pi }{108}}=&{\sqrt[{3}]{\cos {\frac {2\pi }{36}}+i\sin {\frac {2\pi }{36}}}}+{\sqrt[{3}]{\cos {\frac {2\pi }{36}}-i\sin {\frac {2\pi }{36}}}}\\\cos {\frac {2\pi }{108}}=&{\frac {{\sqrt[{3}]{\sqrt[{3}]{\frac {{\sqrt {3}}+i}{2}}}}+{\sqrt[{3}]{\sqrt[{3}]{\frac {{\sqrt {3}}-i}{2}}}}}{2}}={\frac {{\sqrt[{3}]{\sqrt[{3}]{-i\omega }}}+{\sqrt[{3}]{\sqrt[{3}]{i\omega ^{2}}}}}{2}}\end{aligned}}}