百八十角形
x 1 = 2 cos  2 π 180 + 2 cos  122 π 180 + 2 cos  118 π 180 = 0 x 2 = 2 cos  26 π 180 + 2 cos  146 π 180 + 2 cos  94 π 180 = 0 x 3 = 2 cos  14 π 180 + 2 cos  134 π 180 + 2 cos  106 π 180 = 0 x 4 = 2 cos  178 π 180 + 2 cos  58 π 180 + 2 cos  62 π 180 = 0 x 5 = 2 cos  98 π 180 + 2 cos  142 π 180 + 2 cos  22 π 180 = 0 x 6 = 2 cos  166 π 180 + 2 cos  46 π 180 + 2 cos  74 π 180 = 0 x 7 = 2 cos  34 π 180 + 2 cos  86 π 180 + 2 cos  154 π 180 = 0 x 8 = 2 cos  82 π 180 + 2 cos  38 π 180 + 2 cos  158 π 180 = 0 {\displaystyle {\begin{aligned}&x_{1}=2\cos {\frac {2\pi }{180}}+2\cos {\frac {122\pi }{180}}+2\cos {\frac {118\pi }{180}}=0\\&x_{2}=2\cos {\frac {26\pi }{180}}+2\cos {\frac {146\pi }{180}}+2\cos {\frac {94\pi }{180}}=0\\&x_{3}=2\cos {\frac {14\pi }{180}}+2\cos {\frac {134\pi }{180}}+2\cos {\frac {106\pi }{180}}=0\\&x_{4}=2\cos {\frac {178\pi }{180}}+2\cos {\frac {58\pi }{180}}+2\cos {\frac {62\pi }{180}}=0\\&x_{5}=2\cos {\frac {98\pi }{180}}+2\cos {\frac {142\pi }{180}}+2\cos {\frac {22\pi }{180}}=0\\&x_{6}=2\cos {\frac {166\pi }{180}}+2\cos {\frac {46\pi }{180}}+2\cos {\frac {74\pi }{180}}=0\\&x_{7}=2\cos {\frac {34\pi }{180}}+2\cos {\frac {86\pi }{180}}+2\cos {\frac {154\pi }{180}}=0\\&x_{8}=2\cos {\frac {82\pi }{180}}+2\cos {\frac {38\pi }{180}}+2\cos {\frac {158\pi }{180}}=0\\\end{aligned}}}
u 1 = 2 cos  2 π 180 = cos  2 π 60 + i sin  2 π 60 3 + cos  2 π 60 − i sin  2 π 60 3 4 cos  2 π 180 = 8 cos  2 π 60 + i 8 sin  2 π 60 3 + 8 cos  2 π 60 − i 8 sin  2 π 60 3 4 cos  2 π 180 = 10 − 20 + 3 + 15 + i ⋅ ( 30 − 180 − 5 − 1 ) 3 + 10 − 20 + 3 + 15 − i ⋅ ( 30 − 180 − 5 − 1 ) 3 {\displaystyle {\begin{aligned}u_{1}=2\cos {\frac {2\pi }{180}}=&{\sqrt[{3}]{\cos {\frac {2\pi }{60}}+i\sin {\frac {2\pi }{60}}}}+{\sqrt[{3}]{\cos {\frac {2\pi }{60}}-i\sin {\frac {2\pi }{60}}}}\\4\cos {\frac {2\pi }{180}}=&{\sqrt[{3}]{8\cos {\frac {2\pi }{60}}+i8\sin {\frac {2\pi }{60}}}}+{\sqrt[{3}]{8\cos {\frac {2\pi }{60}}-i8\sin {\frac {2\pi }{60}}}}\\4\cos {\frac {2\pi }{180}}=&{\sqrt[{3}]{{\sqrt {10-{\sqrt {20}}}}+{\sqrt {3}}+{\sqrt {15}}+i\cdot ({\sqrt {30-{\sqrt {180}}}}-{\sqrt {5}}-1)}}+{\sqrt[{3}]{{\sqrt {10-{\sqrt {20}}}}+{\sqrt {3}}+{\sqrt {15}}-i\cdot ({\sqrt {30-{\sqrt {180}}}}-{\sqrt {5}}-1)}}\\\end{aligned}}}