二十五角形
cos  2 π 25 = 1 2 ( 5 − 1 4 + 10 + 2 5 4 i 5 + 5 − 1 4 − 10 + 2 5 4 i 5 ) = 1 2 ( cos  2 π 5 + i ⋅ sin  2 π 5 5 + cos  2 π 5 − i ⋅ sin  2 π 5 5 ) {\displaystyle \cos {\frac {2\pi }{25}}={\frac {1}{2}}\left({\sqrt[{5}]{{\frac {{\sqrt {5}}-1}{4}}+{\frac {\sqrt {10+2{\sqrt {5}}}}{4}}i}}+{\sqrt[{5}]{{\frac {{\sqrt {5}}-1}{4}}-{\frac {\sqrt {10+2{\sqrt {5}}}}{4}}i}}\right)={\frac {1}{2}}\left({\sqrt[{5}]{\cos {\frac {2\pi }{5}}+i\cdot \sin {\frac {2\pi }{5}}}}+{\sqrt[{5}]{\cos {\frac {2\pi }{5}}-i\cdot \sin {\frac {2\pi }{5}}}}\right)}