八十四角形
( 2 cos  2 π 84 + ω ⋅ 2 cos  74 π 84 + ω 2 ⋅ 2 cos  50 π 84 ) 3 = 3 x 1 + 2 cos  2 π 28 + 2 cos  6 π 28 + 2 cos  18 π 28 + 6 ( x 4 ) + 3 ω ( 2 x 1 + 6 cos  10 π 12 + 2 cos  10 π 28 + 2 cos  26 π 28 + 2 cos  22 π 28 ) + 3 ω 2 ( 2 x 1 + x 4 + 2 cos  2 π 28 + 2 cos  6 π 28 + 2 cos  18 π 28 ) = 11 3 + 9 7 − 3 3 ( 7 3 + 5 7 ) i 4 ( 2 cos  2 π 84 + ω 2 ⋅ 2 cos  74 π 84 + ω ⋅ 2 cos  50 π 84 ) 3 = 3 x 1 + 2 cos  2 π 28 + 2 cos  6 π 28 + 2 cos  18 π 28 + 6 ( x 4 ) + 3 ω 2 ( 2 x 1 + 6 cos  10 π 12 + 2 cos  10 π 28 + 2 cos  26 π 28 + 2 cos  22 π 28 ) + 3 ω ( 2 x 1 + x 4 + 2 cos  2 π 28 + 2 cos  6 π 28 + 2 cos  18 π 28 ) = 11 3 + 9 7 + 3 3 ( 7 3 + 5 7 ) i 4 {\displaystyle {\begin{aligned}\left(2\cos {\frac {2\pi }{84}}+\omega \cdot 2\cos {\frac {74\pi }{84}}+\omega ^{2}\cdot 2\cos {\frac {50\pi }{84}}\right)^{3}=&3x_{1}+2\cos {\frac {2\pi }{28}}+2\cos {\frac {6\pi }{28}}+2\cos {\frac {18\pi }{28}}+6(x_{4})+3\omega \left(2x_{1}+6\cos {\frac {10\pi }{12}}+2\cos {\frac {10\pi }{28}}+2\cos {\frac {26\pi }{28}}+2\cos {\frac {22\pi }{28}}\right)+3\omega ^{2}\left(2x_{1}+x_{4}+2\cos {\frac {2\pi }{28}}+2\cos {\frac {6\pi }{28}}+2\cos {\frac {18\pi }{28}}\right)\\=&{\frac {11{\sqrt {3}}+9{\sqrt {7}}-3{\sqrt {3}}(7{\sqrt {3}}+5{\sqrt {7}})i}{4}}\\\left(2\cos {\frac {2\pi }{84}}+\omega ^{2}\cdot 2\cos {\frac {74\pi }{84}}+\omega \cdot 2\cos {\frac {50\pi }{84}}\right)^{3}=&3x_{1}+2\cos {\frac {2\pi }{28}}+2\cos {\frac {6\pi }{28}}+2\cos {\frac {18\pi }{28}}+6(x_{4})+3\omega ^{2}\left(2x_{1}+6\cos {\frac {10\pi }{12}}+2\cos {\frac {10\pi }{28}}+2\cos {\frac {26\pi }{28}}+2\cos {\frac {22\pi }{28}}\right)+3\omega \left(2x_{1}+x_{4}+2\cos {\frac {2\pi }{28}}+2\cos {\frac {6\pi }{28}}+2\cos {\frac {18\pi }{28}}\right)\\=&{\frac {11{\sqrt {3}}+9{\sqrt {7}}+3{\sqrt {3}}(7{\sqrt {3}}+5{\sqrt {7}})i}{4}}\\\end{aligned}}}