Подробное решение
Дано уравнение
cos 22 ( x ) = 2 \cos^{22}{\left(x \right)} = 2 cos 22 ( x ) = 2 преобразуем
cos 22 ( x ) − 2 = 0 \cos^{22}{\left(x \right)} - 2 = 0 cos 22 ( x ) − 2 = 0 cos 22 ( x ) − 2 = 0 \cos^{22}{\left(x \right)} - 2 = 0 cos 22 ( x ) − 2 = 0 Сделаем замену
w = cos ( x ) w = \cos{\left(x \right)} w = cos ( x ) Дано уравнение
w 22 − 2 = 0 w^{22} - 2 = 0 w 22 − 2 = 0 Т.к. степень в уравнении равна = 22 - содержит чётное число 22 в числителе, то
уравнение будет иметь два действительных корня.
Извлечём корень 22-й степени из обеих частей уравнения:
Получим:
( 1 w + 0 ) 22 22 = 2 22 \sqrt[22]{\left(1 w + 0\right)^{22}} = \sqrt[22]{2} 22 ( 1 w + 0 ) 22 = 22 2 ( 1 w + 0 ) 22 22 = − 2 22 \sqrt[22]{\left(1 w + 0\right)^{22}} = - \sqrt[22]{2} 22 ( 1 w + 0 ) 22 = − 22 2 или
w = 2 22 w = \sqrt[22]{2} w = 22 2 w = − 2 22 w = - \sqrt[22]{2} w = − 22 2 Раскрываем скобочки в правой части уравнения
w = 2^1/22 Получим ответ: w = 2^(1/22)
Раскрываем скобочки в правой части уравнения
w = -2^1/22 Получим ответ: w = -2^(1/22)
или
w 1 = − 2 22 w_{1} = - \sqrt[22]{2} w 1 = − 22 2 w 2 = 2 22 w_{2} = \sqrt[22]{2} w 2 = 22 2 Остальные 20 корня(ей) являются комплексными.
сделаем замену:
z = w z = w z = w тогда уравнение будет таким:
z 22 = 2 z^{22} = 2 z 22 = 2 Любое комплексное число можно представить так:
z = r e i p z = r e^{i p} z = r e i p подставляем в уравнение
r 22 e 22 i p = 2 r^{22} e^{22 i p} = 2 r 22 e 22 i p = 2 где
r = 2 22 r = \sqrt[22]{2} r = 22 2 - модуль комплексного числа
Подставляем r:
e 22 i p = 1 e^{22 i p} = 1 e 22 i p = 1 Используя формулу Эйлера, найдём корни для p
i sin ( 22 p ) + cos ( 22 p ) = 1 i \sin{\left(22 p \right)} + \cos{\left(22 p \right)} = 1 i sin ( 22 p ) + cos ( 22 p ) = 1 значит
cos ( 22 p ) = 1 \cos{\left(22 p \right)} = 1 cos ( 22 p ) = 1 и
sin ( 22 p ) = 0 \sin{\left(22 p \right)} = 0 sin ( 22 p ) = 0 тогда
p = π N 11 p = \frac{\pi N}{11} p = 11 π N где N=0,1,2,3,...
Перебирая значения N и подставив p в формулу для z
Значит, решением будет для z:
z 1 = − 2 22 z_{1} = - \sqrt[22]{2} z 1 = − 22 2 z 2 = 2 22 z_{2} = \sqrt[22]{2} z 2 = 22 2 z 3 = − 2 22 cos ( π 11 ) − 2 22 i sin ( π 11 ) z_{3} = - \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)} z 3 = − 22 2 cos ( 11 π ) − 22 2 i sin ( 11 π ) z 4 = − 2 22 cos ( π 11 ) + 2 22 i sin ( π 11 ) z_{4} = - \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)} z 4 = − 22 2 cos ( 11 π ) + 22 2 i sin ( 11 π ) z 5 = 2 22 cos ( π 11 ) − 2 22 i sin ( π 11 ) z_{5} = \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)} z 5 = 22 2 cos ( 11 π ) − 22 2 i sin ( 11 π ) z 6 = 2 22 cos ( π 11 ) + 2 22 i sin ( π 11 ) z_{6} = \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)} z 6 = 22 2 cos ( 11 π ) + 22 2 i sin ( 11 π ) z 7 = − 2 22 cos ( 2 π 11 ) − 2 22 i sin ( 2 π 11 ) z_{7} = - \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)} z 7 = − 22 2 cos ( 11 2 π ) − 22 2 i sin ( 11 2 π ) z 8 = − 2 22 cos ( 2 π 11 ) + 2 22 i sin ( 2 π 11 ) z_{8} = - \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)} z 8 = − 22 2 cos ( 11 2 π ) + 22 2 i sin ( 11 2 π ) z 9 = 2 22 cos ( 2 π 11 ) − 2 22 i sin ( 2 π 11 ) z_{9} = \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)} z 9 = 22 2 cos ( 11 2 π ) − 22 2 i sin ( 11 2 π ) z 10 = 2 22 cos ( 2 π 11 ) + 2 22 i sin ( 2 π 11 ) z_{10} = \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)} z 10 = 22 2 cos ( 11 2 π ) + 22 2 i sin ( 11 2 π ) z 11 = − 2 22 cos ( 3 π 11 ) − 2 22 i sin ( 3 π 11 ) z_{11} = - \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)} z 11 = − 22 2 cos ( 11 3 π ) − 22 2 i sin ( 11 3 π ) z 12 = − 2 22 cos ( 3 π 11 ) + 2 22 i sin ( 3 π 11 ) z_{12} = - \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)} z 12 = − 22 2 cos ( 11 3 π ) + 22 2 i sin ( 11 3 π ) z 13 = 2 22 cos ( 3 π 11 ) − 2 22 i sin ( 3 π 11 ) z_{13} = \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)} z 13 = 22 2 cos ( 11 3 π ) − 22 2 i sin ( 11 3 π ) z 14 = 2 22 cos ( 3 π 11 ) + 2 22 i sin ( 3 π 11 ) z_{14} = \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)} z 14 = 22 2 cos ( 11 3 π ) + 22 2 i sin ( 11 3 π ) z 15 = − 2 22 cos ( 4 π 11 ) − 2 22 i sin ( 4 π 11 ) z_{15} = - \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)} z 15 = − 22 2 cos ( 11 4 π ) − 22 2 i sin ( 11 4 π ) z 16 = − 2 22 cos ( 4 π 11 ) + 2 22 i sin ( 4 π 11 ) z_{16} = - \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)} z 16 = − 22 2 cos ( 11 4 π ) + 22 2 i sin ( 11 4 π ) z 17 = 2 22 cos ( 4 π 11 ) − 2 22 i sin ( 4 π 11 ) z_{17} = \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)} z 17 = 22 2 cos ( 11 4 π ) − 22 2 i sin ( 11 4 π ) z 18 = 2 22 cos ( 4 π 11 ) + 2 22 i sin ( 4 π 11 ) z_{18} = \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)} z 18 = 22 2 cos ( 11 4 π ) + 22 2 i sin ( 11 4 π ) z 19 = − 2 22 cos ( 5 π 11 ) − 2 22 i sin ( 5 π 11 ) z_{19} = - \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)} z 19 = − 22 2 cos ( 11 5 π ) − 22 2 i sin ( 11 5 π ) z 20 = − 2 22 cos ( 5 π 11 ) + 2 22 i sin ( 5 π 11 ) z_{20} = - \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)} z 20 = − 22 2 cos ( 11 5 π ) + 22 2 i sin ( 11 5 π ) z 21 = 2 22 cos ( 5 π 11 ) − 2 22 i sin ( 5 π 11 ) z_{21} = \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)} z 21 = 22 2 cos ( 11 5 π ) − 22 2 i sin ( 11 5 π ) z 22 = 2 22 cos ( 5 π 11 ) + 2 22 i sin ( 5 π 11 ) z_{22} = \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)} z 22 = 22 2 cos ( 11 5 π ) + 22 2 i sin ( 11 5 π ) делаем обратную замену
z = w z = w z = w w = z w = z w = z Тогда, окончательный ответ:
w 1 = − 2 22 w_{1} = - \sqrt[22]{2} w 1 = − 22 2 w 2 = 2 22 w_{2} = \sqrt[22]{2} w 2 = 22 2 w 3 = − 2 22 cos ( π 11 ) − 2 22 i sin ( π 11 ) w_{3} = - \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)} w 3 = − 22 2 cos ( 11 π ) − 22 2 i sin ( 11 π ) w 4 = − 2 22 cos ( π 11 ) + 2 22 i sin ( π 11 ) w_{4} = - \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)} w 4 = − 22 2 cos ( 11 π ) + 22 2 i sin ( 11 π ) w 5 = 2 22 cos ( π 11 ) − 2 22 i sin ( π 11 ) w_{5} = \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)} w 5 = 22 2 cos ( 11 π ) − 22 2 i sin ( 11 π ) w 6 = 2 22 cos ( π 11 ) + 2 22 i sin ( π 11 ) w_{6} = \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)} w 6 = 22 2 cos ( 11 π ) + 22 2 i sin ( 11 π ) w 7 = − 2 22 cos ( 2 π 11 ) − 2 22 i sin ( 2 π 11 ) w_{7} = - \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)} w 7 = − 22 2 cos ( 11 2 π ) − 22 2 i sin ( 11 2 π ) w 8 = − 2 22 cos ( 2 π 11 ) + 2 22 i sin ( 2 π 11 ) w_{8} = - \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)} w 8 = − 22 2 cos ( 11 2 π ) + 22 2 i sin ( 11 2 π ) w 9 = 2 22 cos ( 2 π 11 ) − 2 22 i sin ( 2 π 11 ) w_{9} = \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)} w 9 = 22 2 cos ( 11 2 π ) − 22 2 i sin ( 11 2 π ) w 10 = 2 22 cos ( 2 π 11 ) + 2 22 i sin ( 2 π 11 ) w_{10} = \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)} w 10 = 22 2 cos ( 11 2 π ) + 22 2 i sin ( 11 2 π ) w 11 = − 2 22 cos ( 3 π 11 ) − 2 22 i sin ( 3 π 11 ) w_{11} = - \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)} w 11 = − 22 2 cos ( 11 3 π ) − 22 2 i sin ( 11 3 π ) w 12 = − 2 22 cos ( 3 π 11 ) + 2 22 i sin ( 3 π 11 ) w_{12} = - \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)} w 12 = − 22 2 cos ( 11 3 π ) + 22 2 i sin ( 11 3 π ) w 13 = 2 22 cos ( 3 π 11 ) − 2 22 i sin ( 3 π 11 ) w_{13} = \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)} w 13 = 22 2 cos ( 11 3 π ) − 22 2 i sin ( 11 3 π ) w 14 = 2 22 cos ( 3 π 11 ) + 2 22 i sin ( 3 π 11 ) w_{14} = \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)} w 14 = 22 2 cos ( 11 3 π ) + 22 2 i sin ( 11 3 π ) w 15 = − 2 22 cos ( 4 π 11 ) − 2 22 i sin ( 4 π 11 ) w_{15} = - \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)} w 15 = − 22 2 cos ( 11 4 π ) − 22 2 i sin ( 11 4 π ) w 16 = − 2 22 cos ( 4 π 11 ) + 2 22 i sin ( 4 π 11 ) w_{16} = - \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)} w 16 = − 22 2 cos ( 11 4 π ) + 22 2 i sin ( 11 4 π ) w 17 = 2 22 cos ( 4 π 11 ) − 2 22 i sin ( 4 π 11 ) w_{17} = \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)} w 17 = 22 2 cos ( 11 4 π ) − 22 2 i sin ( 11 4 π ) w 18 = 2 22 cos ( 4 π 11 ) + 2 22 i sin ( 4 π 11 ) w_{18} = \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)} w 18 = 22 2 cos ( 11 4 π ) + 22 2 i sin ( 11 4 π ) w 19 = − 2 22 cos ( 5 π 11 ) − 2 22 i sin ( 5 π 11 ) w_{19} = - \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)} w 19 = − 22 2 cos ( 11 5 π ) − 22 2 i sin ( 11 5 π ) w 20 = − 2 22 cos ( 5 π 11 ) + 2 22 i sin ( 5 π 11 ) w_{20} = - \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)} w 20 = − 22 2 cos ( 11 5 π ) + 22 2 i sin ( 11 5 π ) w 21 = 2 22 cos ( 5 π 11 ) − 2 22 i sin ( 5 π 11 ) w_{21} = \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)} w 21 = 22 2 cos ( 11 5 π ) − 22 2 i sin ( 11 5 π ) w 22 = 2 22 cos ( 5 π 11 ) + 2 22 i sin ( 5 π 11 ) w_{22} = \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)} w 22 = 22 2 cos ( 11 5 π ) + 22 2 i sin ( 11 5 π ) делаем обратную замену
cos ( x ) = w \cos{\left(x \right)} = w cos ( x ) = w cos ( x ) = w \cos{\left(x \right)} = w cos ( x ) = w - это простейшее тригонометрическое уравнение
Это уравнение преобразуется в
x = 2 π n + acos ( w ) x = 2 \pi n + \operatorname{acos}{\left(w \right)} x = 2 πn + acos ( w ) x = 2 π n + acos ( w ) − π x = 2 \pi n + \operatorname{acos}{\left(w \right)} - \pi x = 2 πn + acos ( w ) − π Или
x = 2 π n + acos ( w ) x = 2 \pi n + \operatorname{acos}{\left(w \right)} x = 2 πn + acos ( w ) x = 2 π n + acos ( w ) − π x = 2 \pi n + \operatorname{acos}{\left(w \right)} - \pi x = 2 πn + acos ( w ) − π , где n - любое целое число
подставляем w:
x 1 = 2 π n + acos ( w 1 ) x_{1} = 2 \pi n + \operatorname{acos}{\left(w_{1} \right)} x 1 = 2 πn + acos ( w 1 ) x 1 = 2 π n + acos ( 2 22 ) x_{1} = 2 \pi n + \operatorname{acos}{\left(\sqrt[22]{2} \right)} x 1 = 2 πn + acos ( 22 2 ) x 1 = 2 π n + acos ( 2 22 ) x_{1} = 2 \pi n + \operatorname{acos}{\left(\sqrt[22]{2} \right)} x 1 = 2 πn + acos ( 22 2 ) x 2 = 2 π n + acos ( w 2 ) x_{2} = 2 \pi n + \operatorname{acos}{\left(w_{2} \right)} x 2 = 2 πn + acos ( w 2 ) x 2 = 2 π n + acos ( − 2 22 ) x_{2} = 2 \pi n + \operatorname{acos}{\left(- \sqrt[22]{2} \right)} x 2 = 2 πn + acos ( − 22 2 ) x 2 = 2 π n + acos ( − 2 22 ) x_{2} = 2 \pi n + \operatorname{acos}{\left(- \sqrt[22]{2} \right)} x 2 = 2 πn + acos ( − 22 2 ) x 3 = 2 π n + acos ( w 1 ) − π x_{3} = 2 \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi x 3 = 2 πn + acos ( w 1 ) − π x 3 = 2 π n − π + acos ( 2 22 ) x_{3} = 2 \pi n - \pi + \operatorname{acos}{\left(\sqrt[22]{2} \right)} x 3 = 2 πn − π + acos ( 22 2 ) x 3 = 2 π n − π + acos ( 2 22 ) x_{3} = 2 \pi n - \pi + \operatorname{acos}{\left(\sqrt[22]{2} \right)} x 3 = 2 πn − π + acos ( 22 2 ) x 4 = 2 π n + acos ( w 2 ) − π x_{4} = 2 \pi n + \operatorname{acos}{\left(w_{2} \right)} - \pi x 4 = 2 πn + acos ( w 2 ) − π x 4 = 2 π n − π + acos ( − 2 22 ) x_{4} = 2 \pi n - \pi + \operatorname{acos}{\left(- \sqrt[22]{2} \right)} x 4 = 2 πn − π + acos ( − 22 2 ) x 4 = 2 π n − π + acos ( − 2 22 ) x_{4} = 2 \pi n - \pi + \operatorname{acos}{\left(- \sqrt[22]{2} \right)} x 4 = 2 πn − π + acos ( − 22 2 )
/ / 22___\\ / / 22___\\
x_1 = - re\acos\-\/ 2 // + 2*pi - I*im\acos\-\/ 2 //
x 1 = − re ( acos ( − 2 22 ) ) + 2 π − i im ( acos ( − 2 22 ) ) x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \right)}\right)} x 1 = − re ( acos ( − 22 2 ) ) + 2 π − i im ( acos ( − 22 2 ) )
/ /22___\\
x_2 = 2*pi - I*im\acos\\/ 2 //
x 2 = 2 π − i im ( acos ( 2 22 ) ) x_{2} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \right)}\right)} x 2 = 2 π − i im ( acos ( 22 2 ) )
/ / 11____ 22___\\ / / 11____ 22___\\
x_3 = - re\acos\-\/ -1 *\/ 2 // + 2*pi - I*im\acos\-\/ -1 *\/ 2 //
x 3 = − re ( acos ( − − 1 11 ⋅ 2 22 ) ) + 2 π − i im ( acos ( − − 1 11 ⋅ 2 22 ) ) x_{3} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)} x 3 = − re ( acos ( − 11 − 1 ⋅ 22 2 ) ) + 2 π − i im ( acos ( − 11 − 1 ⋅ 22 2 ) )
/ / 9/22 22___\\ 3*pi / / 9/22 22___\\
x_4 = - im\asinh\(-1) *\/ 2 // + ---- + I*re\asinh\(-1) *\/ 2 //
2
x 4 = − im ( asinh ( ( − 1 ) 9 22 ⋅ 2 22 ) ) + 3 π 2 + i re ( asinh ( ( − 1 ) 9 22 ⋅ 2 22 ) ) x_{4} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 4 = − im ( asinh ( ( − 1 ) 22 9 ⋅ 22 2 ) ) + 2 3 π + i re ( asinh ( ( − 1 ) 22 9 ⋅ 22 2 ) )
3*pi / / 9/22 22___\\ / / 9/22 22___\\
x_5 = ---- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
x 5 = im ( asinh ( ( − 1 ) 9 22 ⋅ 2 22 ) ) + 3 π 2 − i re ( asinh ( ( − 1 ) 9 22 ⋅ 2 22 ) ) x_{5} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 5 = im ( asinh ( ( − 1 ) 22 9 ⋅ 22 2 ) ) + 2 3 π − i re ( asinh ( ( − 1 ) 22 9 ⋅ 22 2 ) )
/ /11____ 22___\\ / /11____ 22___\\
x_6 = - re\acos\\/ -1 *\/ 2 // + 2*pi - I*im\acos\\/ -1 *\/ 2 //
x 6 = − re ( acos ( − 1 11 ⋅ 2 22 ) ) + 2 π − i im ( acos ( − 1 11 ⋅ 2 22 ) ) x_{6} = - \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)} x 6 = − re ( acos ( 11 − 1 ⋅ 22 2 ) ) + 2 π − i im ( acos ( 11 − 1 ⋅ 22 2 ) )
/ / 2/11 22___\\ / / 2/11 22___\\
x_7 = - re\acos\-(-1) *\/ 2 // + 2*pi - I*im\acos\-(-1) *\/ 2 //
x 7 = − re ( acos ( − ( − 1 ) 2 11 ⋅ 2 22 ) ) + 2 π − i im ( acos ( − ( − 1 ) 2 11 ⋅ 2 22 ) ) x_{7} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)} x 7 = − re ( acos ( − ( − 1 ) 11 2 ⋅ 22 2 ) ) + 2 π − i im ( acos ( − ( − 1 ) 11 2 ⋅ 22 2 ) )
/ / 7/22 22___\\ 3*pi / / 7/22 22___\\
x_8 = - im\asinh\(-1) *\/ 2 // + ---- + I*re\asinh\(-1) *\/ 2 //
2
x 8 = − im ( asinh ( ( − 1 ) 7 22 ⋅ 2 22 ) ) + 3 π 2 + i re ( asinh ( ( − 1 ) 7 22 ⋅ 2 22 ) ) x_{8} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 8 = − im ( asinh ( ( − 1 ) 22 7 ⋅ 22 2 ) ) + 2 3 π + i re ( asinh ( ( − 1 ) 22 7 ⋅ 22 2 ) )
3*pi / / 7/22 22___\\ / / 7/22 22___\\
x_9 = ---- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
x 9 = im ( asinh ( ( − 1 ) 7 22 ⋅ 2 22 ) ) + 3 π 2 − i re ( asinh ( ( − 1 ) 7 22 ⋅ 2 22 ) ) x_{9} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 9 = im ( asinh ( ( − 1 ) 22 7 ⋅ 22 2 ) ) + 2 3 π − i re ( asinh ( ( − 1 ) 22 7 ⋅ 22 2 ) )
/ / 2/11 22___\\ / / 2/11 22___\\
x_10 = - re\acos\(-1) *\/ 2 // + 2*pi - I*im\acos\(-1) *\/ 2 //
x 10 = − re ( acos ( ( − 1 ) 2 11 ⋅ 2 22 ) ) + 2 π − i im ( acos ( ( − 1 ) 2 11 ⋅ 2 22 ) ) x_{10} = - \operatorname{re}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)} x 10 = − re ( acos ( ( − 1 ) 11 2 ⋅ 22 2 ) ) + 2 π − i im ( acos ( ( − 1 ) 11 2 ⋅ 22 2 ) )
/ / 22___ / /5*pi\ /5*pi\\\\ / / 22___ / /5*pi\ /5*pi\\\\
x_11 = - re|acos|-\/ 2 *|I*cos|----| + sin|----|||| + 2*pi - I*im|acos|-\/ 2 *|I*cos|----| + sin|----||||
\ \ \ \ 22 / \ 22 //// \ \ \ \ 22 / \ 22 ////
x 11 = − re ( acos ( − 2 22 ( sin ( 5 π 22 ) + i cos ( 5 π 22 ) ) ) ) + 2 π − i im ( acos ( − 2 22 ( sin ( 5 π 22 ) + i cos ( 5 π 22 ) ) ) ) x_{11} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{5 \pi}{22} \right)} + i \cos{\left(\frac{5 \pi}{22} \right)}\right) \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{5 \pi}{22} \right)} + i \cos{\left(\frac{5 \pi}{22} \right)}\right) \right)}\right)} x 11 = − re ( acos ( − 22 2 ( sin ( 22 5 π ) + i cos ( 22 5 π ) ) ) ) + 2 π − i im ( acos ( − 22 2 ( sin ( 22 5 π ) + i cos ( 22 5 π ) ) ) )
/ / 5/22 22___\\ 3*pi / / 5/22 22___\\
x_12 = - im\asinh\(-1) *\/ 2 // + ---- + I*re\asinh\(-1) *\/ 2 //
2
x 12 = − im ( asinh ( ( − 1 ) 5 22 ⋅ 2 22 ) ) + 3 π 2 + i re ( asinh ( ( − 1 ) 5 22 ⋅ 2 22 ) ) x_{12} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 12 = − im ( asinh ( ( − 1 ) 22 5 ⋅ 22 2 ) ) + 2 3 π + i re ( asinh ( ( − 1 ) 22 5 ⋅ 22 2 ) )
3*pi / / 5/22 22___\\ / / 5/22 22___\\
x_13 = ---- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
x 13 = im ( asinh ( ( − 1 ) 5 22 ⋅ 2 22 ) ) + 3 π 2 − i re ( asinh ( ( − 1 ) 5 22 ⋅ 2 22 ) ) x_{13} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 13 = im ( asinh ( ( − 1 ) 22 5 ⋅ 22 2 ) ) + 2 3 π − i re ( asinh ( ( − 1 ) 22 5 ⋅ 22 2 ) )
/ / 3/11 22___\\ / / 3/11 22___\\
x_14 = - re\acos\(-1) *\/ 2 // + 2*pi - I*im\acos\(-1) *\/ 2 //
x 14 = − re ( acos ( ( − 1 ) 3 11 ⋅ 2 22 ) ) + 2 π − i im ( acos ( ( − 1 ) 3 11 ⋅ 2 22 ) ) x_{14} = - \operatorname{re}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{3}{11}} \cdot \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{3}{11}} \cdot \sqrt[22]{2} \right)}\right)} x 14 = − re ( acos ( ( − 1 ) 11 3 ⋅ 22 2 ) ) + 2 π − i im ( acos ( ( − 1 ) 11 3 ⋅ 22 2 ) )
/ / 22___ / /3*pi\ /3*pi\\\\ / / 22___ / /3*pi\ /3*pi\\\\
x_15 = - re|acos|-\/ 2 *|I*cos|----| + sin|----|||| + 2*pi - I*im|acos|-\/ 2 *|I*cos|----| + sin|----||||
\ \ \ \ 22 / \ 22 //// \ \ \ \ 22 / \ 22 ////
x 15 = − re ( acos ( − 2 22 ( sin ( 3 π 22 ) + i cos ( 3 π 22 ) ) ) ) + 2 π − i im ( acos ( − 2 22 ( sin ( 3 π 22 ) + i cos ( 3 π 22 ) ) ) ) x_{15} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{3 \pi}{22} \right)} + i \cos{\left(\frac{3 \pi}{22} \right)}\right) \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{3 \pi}{22} \right)} + i \cos{\left(\frac{3 \pi}{22} \right)}\right) \right)}\right)} x 15 = − re ( acos ( − 22 2 ( sin ( 22 3 π ) + i cos ( 22 3 π ) ) ) ) + 2 π − i im ( acos ( − 22 2 ( sin ( 22 3 π ) + i cos ( 22 3 π ) ) ) )
/ / 3/22 22___\\ 3*pi / / 3/22 22___\\
x_16 = - im\asinh\(-1) *\/ 2 // + ---- + I*re\asinh\(-1) *\/ 2 //
2
x 16 = − im ( asinh ( ( − 1 ) 3 22 ⋅ 2 22 ) ) + 3 π 2 + i re ( asinh ( ( − 1 ) 3 22 ⋅ 2 22 ) ) x_{16} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 16 = − im ( asinh ( ( − 1 ) 22 3 ⋅ 22 2 ) ) + 2 3 π + i re ( asinh ( ( − 1 ) 22 3 ⋅ 22 2 ) )
3*pi / / 3/22 22___\\ / / 3/22 22___\\
x_17 = ---- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
x 17 = im ( asinh ( ( − 1 ) 3 22 ⋅ 2 22 ) ) + 3 π 2 − i re ( asinh ( ( − 1 ) 3 22 ⋅ 2 22 ) ) x_{17} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 17 = im ( asinh ( ( − 1 ) 22 3 ⋅ 22 2 ) ) + 2 3 π − i re ( asinh ( ( − 1 ) 22 3 ⋅ 22 2 ) )
/ / 4/11 22___\\ / / 4/11 22___\\
x_18 = - re\acos\(-1) *\/ 2 // + 2*pi - I*im\acos\(-1) *\/ 2 //
x 18 = − re ( acos ( ( − 1 ) 4 11 ⋅ 2 22 ) ) + 2 π − i im ( acos ( ( − 1 ) 4 11 ⋅ 2 22 ) ) x_{18} = - \operatorname{re}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{4}{11}} \cdot \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{4}{11}} \cdot \sqrt[22]{2} \right)}\right)} x 18 = − re ( acos ( ( − 1 ) 11 4 ⋅ 22 2 ) ) + 2 π − i im ( acos ( ( − 1 ) 11 4 ⋅ 22 2 ) )
/ / 22___ / /pi\ /pi\\\\ / / 22___ / /pi\ /pi\\\\
x_19 = - re|acos|-\/ 2 *|I*cos|--| + sin|--|||| + 2*pi - I*im|acos|-\/ 2 *|I*cos|--| + sin|--||||
\ \ \ \22/ \22//// \ \ \ \22/ \22////
x 19 = − re ( acos ( − 2 22 ( sin ( π 22 ) + i cos ( π 22 ) ) ) ) + 2 π − i im ( acos ( − 2 22 ( sin ( π 22 ) + i cos ( π 22 ) ) ) ) x_{19} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} x 19 = − re ( acos ( − 22 2 ( sin ( 22 π ) + i cos ( 22 π ) ) ) ) + 2 π − i im ( acos ( − 22 2 ( sin ( 22 π ) + i cos ( 22 π ) ) ) )
/ /22___ / /pi\ /pi\\\\ / /22___ / /pi\ /pi\\\\
x_20 = - re|acos|\/ 2 *|- sin|--| + I*cos|--|||| + 2*pi - I*im|acos|\/ 2 *|- sin|--| + I*cos|--||||
\ \ \ \22/ \22//// \ \ \ \22/ \22////
x 20 = − re ( acos ( 2 22 ( − sin ( π 22 ) + i cos ( π 22 ) ) ) ) + 2 π − i im ( acos ( 2 22 ( − sin ( π 22 ) + i cos ( π 22 ) ) ) ) x_{20} = - \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(- \sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(- \sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} x 20 = − re ( acos ( 22 2 ( − sin ( 22 π ) + i cos ( 22 π ) ) ) ) + 2 π − i im ( acos ( 22 2 ( − sin ( 22 π ) + i cos ( 22 π ) ) ) )
/ /22___ / /pi\ /pi\\\\ / /22___ / /pi\ /pi\\\\
x_21 = - re|acos|\/ 2 *|- I*cos|--| + sin|--|||| + 2*pi - I*im|acos|\/ 2 *|- I*cos|--| + sin|--||||
\ \ \ \22/ \22//// \ \ \ \22/ \22////
x 21 = − re ( acos ( 2 22 ( sin ( π 22 ) − i cos ( π 22 ) ) ) ) + 2 π − i im ( acos ( 2 22 ( sin ( π 22 ) − i cos ( π 22 ) ) ) ) x_{21} = - \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} - i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} - i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} x 21 = − re ( acos ( 22 2 ( sin ( 22 π ) − i cos ( 22 π ) ) ) ) + 2 π − i im ( acos ( 22 2 ( sin ( 22 π ) − i cos ( 22 π ) ) ) )
/ /22___ / /pi\ /pi\\\\ / /22___ / /pi\ /pi\\\\
x_22 = - re|acos|\/ 2 *|I*cos|--| + sin|--|||| + 2*pi - I*im|acos|\/ 2 *|I*cos|--| + sin|--||||
\ \ \ \22/ \22//// \ \ \ \22/ \22////
x 22 = − re ( acos ( 2 22 ( sin ( π 22 ) + i cos ( π 22 ) ) ) ) + 2 π − i im ( acos ( 2 22 ( sin ( π 22 ) + i cos ( π 22 ) ) ) ) x_{22} = - \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} x 22 = − re ( acos ( 22 2 ( sin ( 22 π ) + i cos ( 22 π ) ) ) ) + 2 π − i im ( acos ( 22 2 ( sin ( 22 π ) + i cos ( 22 π ) ) ) )
/ / 22___\\ / / 22___\\
x_23 = I*im\acos\-\/ 2 // + re\acos\-\/ 2 //
x 23 = re ( acos ( − 2 22 ) ) + i im ( acos ( − 2 22 ) ) x_{23} = \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \right)}\right)} x 23 = re ( acos ( − 22 2 ) ) + i im ( acos ( − 22 2 ) )
/ /22___\\
x_24 = I*im\acos\\/ 2 //
x 24 = i im ( acos ( 2 22 ) ) x_{24} = i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \right)}\right)} x 24 = i im ( acos ( 22 2 ) )
/ / 11____ 22___\\ / / 11____ 22___\\
x_25 = I*im\acos\-\/ -1 *\/ 2 // + re\acos\-\/ -1 *\/ 2 //
x 25 = re ( acos ( − − 1 11 ⋅ 2 22 ) ) + i im ( acos ( − − 1 11 ⋅ 2 22 ) ) x_{25} = \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)} x 25 = re ( acos ( − 11 − 1 ⋅ 22 2 ) ) + i im ( acos ( − 11 − 1 ⋅ 22 2 ) )
pi / / 9/22 22___\\ / / 9/22 22___\\
x_26 = -- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
x 26 = im ( asinh ( ( − 1 ) 9 22 ⋅ 2 22 ) ) + π 2 − i re ( asinh ( ( − 1 ) 9 22 ⋅ 2 22 ) ) x_{26} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 26 = im ( asinh ( ( − 1 ) 22 9 ⋅ 22 2 ) ) + 2 π − i re ( asinh ( ( − 1 ) 22 9 ⋅ 22 2 ) )
pi / / 9/22 22___\\ / / 9/22 22___\\
x_27 = -- - im\asinh\(-1) *\/ 2 // + I*re\asinh\(-1) *\/ 2 //
2
x 27 = − im ( asinh ( ( − 1 ) 9 22 ⋅ 2 22 ) ) + π 2 + i re ( asinh ( ( − 1 ) 9 22 ⋅ 2 22 ) ) x_{27} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 27 = − im ( asinh ( ( − 1 ) 22 9 ⋅ 22 2 ) ) + 2 π + i re ( asinh ( ( − 1 ) 22 9 ⋅ 22 2 ) )
/ /11____ 22___\\ / /11____ 22___\\
x_28 = I*im\acos\\/ -1 *\/ 2 // + re\acos\\/ -1 *\/ 2 //
x 28 = re ( acos ( − 1 11 ⋅ 2 22 ) ) + i im ( acos ( − 1 11 ⋅ 2 22 ) ) x_{28} = \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)} x 28 = re ( acos ( 11 − 1 ⋅ 22 2 ) ) + i im ( acos ( 11 − 1 ⋅ 22 2 ) )
/ / 2/11 22___\\ / / 2/11 22___\\
x_29 = I*im\acos\-(-1) *\/ 2 // + re\acos\-(-1) *\/ 2 //
x 29 = re ( acos ( − ( − 1 ) 2 11 ⋅ 2 22 ) ) + i im ( acos ( − ( − 1 ) 2 11 ⋅ 2 22 ) ) x_{29} = \operatorname{re}{\left(\operatorname{acos}{\left(- \left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)} x 29 = re ( acos ( − ( − 1 ) 11 2 ⋅ 22 2 ) ) + i im ( acos ( − ( − 1 ) 11 2 ⋅ 22 2 ) )
pi / / 7/22 22___\\ / / 7/22 22___\\
x_30 = -- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
x 30 = im ( asinh ( ( − 1 ) 7 22 ⋅ 2 22 ) ) + π 2 − i re ( asinh ( ( − 1 ) 7 22 ⋅ 2 22 ) ) x_{30} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 30 = im ( asinh ( ( − 1 ) 22 7 ⋅ 22 2 ) ) + 2 π − i re ( asinh ( ( − 1 ) 22 7 ⋅ 22 2 ) )
pi / / 7/22 22___\\ / / 7/22 22___\\
x_31 = -- - im\asinh\(-1) *\/ 2 // + I*re\asinh\(-1) *\/ 2 //
2
x 31 = − im ( asinh ( ( − 1 ) 7 22 ⋅ 2 22 ) ) + π 2 + i re ( asinh ( ( − 1 ) 7 22 ⋅ 2 22 ) ) x_{31} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 31 = − im ( asinh ( ( − 1 ) 22 7 ⋅ 22 2 ) ) + 2 π + i re ( asinh ( ( − 1 ) 22 7 ⋅ 22 2 ) )
/ / 2/11 22___\\ / / 2/11 22___\\
x_32 = I*im\acos\(-1) *\/ 2 // + re\acos\(-1) *\/ 2 //
x 32 = re ( acos ( ( − 1 ) 2 11 ⋅ 2 22 ) ) + i im ( acos ( ( − 1 ) 2 11 ⋅ 2 22 ) ) x_{32} = \operatorname{re}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)} x 32 = re ( acos ( ( − 1 ) 11 2 ⋅ 22 2 ) ) + i im ( acos ( ( − 1 ) 11 2 ⋅ 22 2 ) )
/ / 22___ / /5*pi\ /5*pi\\\\ / / 22___ / /5*pi\ /5*pi\\\\
x_33 = I*im|acos|-\/ 2 *|I*cos|----| + sin|----|||| + re|acos|-\/ 2 *|I*cos|----| + sin|----||||
\ \ \ \ 22 / \ 22 //// \ \ \ \ 22 / \ 22 ////
x 33 = re ( acos ( − 2 22 ( sin ( 5 π 22 ) + i cos ( 5 π 22 ) ) ) ) + i im ( acos ( − 2 22 ( sin ( 5 π 22 ) + i cos ( 5 π 22 ) ) ) ) x_{33} = \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{5 \pi}{22} \right)} + i \cos{\left(\frac{5 \pi}{22} \right)}\right) \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{5 \pi}{22} \right)} + i \cos{\left(\frac{5 \pi}{22} \right)}\right) \right)}\right)} x 33 = re ( acos ( − 22 2 ( sin ( 22 5 π ) + i cos ( 22 5 π ) ) ) ) + i im ( acos ( − 22 2 ( sin ( 22 5 π ) + i cos ( 22 5 π ) ) ) )
pi / / 5/22 22___\\ / / 5/22 22___\\
x_34 = -- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
x 34 = im ( asinh ( ( − 1 ) 5 22 ⋅ 2 22 ) ) + π 2 − i re ( asinh ( ( − 1 ) 5 22 ⋅ 2 22 ) ) x_{34} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 34 = im ( asinh ( ( − 1 ) 22 5 ⋅ 22 2 ) ) + 2 π − i re ( asinh ( ( − 1 ) 22 5 ⋅ 22 2 ) )
pi / / 5/22 22___\\ / / 5/22 22___\\
x_35 = -- - im\asinh\(-1) *\/ 2 // + I*re\asinh\(-1) *\/ 2 //
2
x 35 = − im ( asinh ( ( − 1 ) 5 22 ⋅ 2 22 ) ) + π 2 + i re ( asinh ( ( − 1 ) 5 22 ⋅ 2 22 ) ) x_{35} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 35 = − im ( asinh ( ( − 1 ) 22 5 ⋅ 22 2 ) ) + 2 π + i re ( asinh ( ( − 1 ) 22 5 ⋅ 22 2 ) )
/ / 3/11 22___\\ / / 3/11 22___\\
x_36 = I*im\acos\(-1) *\/ 2 // + re\acos\(-1) *\/ 2 //
x 36 = re ( acos ( ( − 1 ) 3 11 ⋅ 2 22 ) ) + i im ( acos ( ( − 1 ) 3 11 ⋅ 2 22 ) ) x_{36} = \operatorname{re}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{3}{11}} \cdot \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{3}{11}} \cdot \sqrt[22]{2} \right)}\right)} x 36 = re ( acos ( ( − 1 ) 11 3 ⋅ 22 2 ) ) + i im ( acos ( ( − 1 ) 11 3 ⋅ 22 2 ) )
/ / 22___ / /3*pi\ /3*pi\\\\ / / 22___ / /3*pi\ /3*pi\\\\
x_37 = I*im|acos|-\/ 2 *|I*cos|----| + sin|----|||| + re|acos|-\/ 2 *|I*cos|----| + sin|----||||
\ \ \ \ 22 / \ 22 //// \ \ \ \ 22 / \ 22 ////
x 37 = re ( acos ( − 2 22 ( sin ( 3 π 22 ) + i cos ( 3 π 22 ) ) ) ) + i im ( acos ( − 2 22 ( sin ( 3 π 22 ) + i cos ( 3 π 22 ) ) ) ) x_{37} = \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{3 \pi}{22} \right)} + i \cos{\left(\frac{3 \pi}{22} \right)}\right) \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{3 \pi}{22} \right)} + i \cos{\left(\frac{3 \pi}{22} \right)}\right) \right)}\right)} x 37 = re ( acos ( − 22 2 ( sin ( 22 3 π ) + i cos ( 22 3 π ) ) ) ) + i im ( acos ( − 22 2 ( sin ( 22 3 π ) + i cos ( 22 3 π ) ) ) )
pi / / 3/22 22___\\ / / 3/22 22___\\
x_38 = -- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
x 38 = im ( asinh ( ( − 1 ) 3 22 ⋅ 2 22 ) ) + π 2 − i re ( asinh ( ( − 1 ) 3 22 ⋅ 2 22 ) ) x_{38} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 38 = im ( asinh ( ( − 1 ) 22 3 ⋅ 22 2 ) ) + 2 π − i re ( asinh ( ( − 1 ) 22 3 ⋅ 22 2 ) )
pi / / 3/22 22___\\ / / 3/22 22___\\
x_39 = -- - im\asinh\(-1) *\/ 2 // + I*re\asinh\(-1) *\/ 2 //
2
x 39 = − im ( asinh ( ( − 1 ) 3 22 ⋅ 2 22 ) ) + π 2 + i re ( asinh ( ( − 1 ) 3 22 ⋅ 2 22 ) ) x_{39} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)} x 39 = − im ( asinh ( ( − 1 ) 22 3 ⋅ 22 2 ) ) + 2 π + i re ( asinh ( ( − 1 ) 22 3 ⋅ 22 2 ) )
/ / 4/11 22___\\ / / 4/11 22___\\
x_40 = I*im\acos\(-1) *\/ 2 // + re\acos\(-1) *\/ 2 //
x 40 = re ( acos ( ( − 1 ) 4 11 ⋅ 2 22 ) ) + i im ( acos ( ( − 1 ) 4 11 ⋅ 2 22 ) ) x_{40} = \operatorname{re}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{4}{11}} \cdot \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{4}{11}} \cdot \sqrt[22]{2} \right)}\right)} x 40 = re ( acos ( ( − 1 ) 11 4 ⋅ 22 2 ) ) + i im ( acos ( ( − 1 ) 11 4 ⋅ 22 2 ) )
/ / 22___ / /pi\ /pi\\\\ / / 22___ / /pi\ /pi\\\\
x_41 = I*im|acos|-\/ 2 *|I*cos|--| + sin|--|||| + re|acos|-\/ 2 *|I*cos|--| + sin|--||||
\ \ \ \22/ \22//// \ \ \ \22/ \22////
x 41 = re ( acos ( − 2 22 ( sin ( π 22 ) + i cos ( π 22 ) ) ) ) + i im ( acos ( − 2 22 ( sin ( π 22 ) + i cos ( π 22 ) ) ) ) x_{41} = \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} x 41 = re ( acos ( − 22 2 ( sin ( 22 π ) + i cos ( 22 π ) ) ) ) + i im ( acos ( − 22 2 ( sin ( 22 π ) + i cos ( 22 π ) ) ) )
/ /22___ / /pi\ /pi\\\\ / /22___ / /pi\ /pi\\\\
x_42 = I*im|acos|\/ 2 *|- sin|--| + I*cos|--|||| + re|acos|\/ 2 *|- sin|--| + I*cos|--||||
\ \ \ \22/ \22//// \ \ \ \22/ \22////
x 42 = re ( acos ( 2 22 ( − sin ( π 22 ) + i cos ( π 22 ) ) ) ) + i im ( acos ( 2 22 ( − sin ( π 22 ) + i cos ( π 22 ) ) ) ) x_{42} = \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(- \sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(- \sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} x 42 = re ( acos ( 22 2 ( − sin ( 22 π ) + i cos ( 22 π ) ) ) ) + i im ( acos ( 22 2 ( − sin ( 22 π ) + i cos ( 22 π ) ) ) )
/ /22___ / /pi\ /pi\\\\ / /22___ / /pi\ /pi\\\\
x_43 = I*im|acos|\/ 2 *|- I*cos|--| + sin|--|||| + re|acos|\/ 2 *|- I*cos|--| + sin|--||||
\ \ \ \22/ \22//// \ \ \ \22/ \22////
x 43 = re ( acos ( 2 22 ( sin ( π 22 ) − i cos ( π 22 ) ) ) ) + i im ( acos ( 2 22 ( sin ( π 22 ) − i cos ( π 22 ) ) ) ) x_{43} = \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} - i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} - i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} x 43 = re ( acos ( 22 2 ( sin ( 22 π ) − i cos ( 22 π ) ) ) ) + i im ( acos ( 22 2 ( sin ( 22 π ) − i cos ( 22 π ) ) ) )
/ /22___ / /pi\ /pi\\\\ / /22___ / /pi\ /pi\\\\
x_44 = I*im|acos|\/ 2 *|I*cos|--| + sin|--|||| + re|acos|\/ 2 *|I*cos|--| + sin|--||||
\ \ \ \22/ \22//// \ \ \ \22/ \22////
x 44 = re ( acos ( 2 22 ( sin ( π 22 ) + i cos ( π 22 ) ) ) ) + i im ( acos ( 2 22 ( sin ( π 22 ) + i cos ( π 22 ) ) ) ) x_{44} = \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} x 44 = re ( acos ( 22 2 ( sin ( 22 π ) + i cos ( 22 π ) ) ) ) + i im ( acos ( 22 2 ( sin ( 22 π ) + i cos ( 22 π ) ) ) )
x1 = 3.14159265358979 + 0.252344872738505*i
x2 = 6.28318530717959 - 0.252344872738505*i
x3 = 3.67671230635564 - 0.543070659697429*i
x4 = 3.67671230635564 + 0.543070659697429*i
x5 = 5.74806565441374 - 0.543070659697429*i
x6 = 5.74806565441374 + 0.543070659697429*i
x7 = 3.95337526139597 - 0.708304870870651*i
x8 = 3.95337526139597 + 0.708304870870651*i
x9 = 5.47140269937341 - 0.708304870870651*i
x10 = 5.47140269937341 + 0.708304870870651*i
x11 = 4.18659554986285 - 0.810160956958411*i
x12 = 4.18659554986285 + 0.810160956958411*i
x13 = 5.23818241090653 - 0.810160956958411*i
x14 = 5.23818241090653 + 0.810160956958411*i
x15 = 4.40213281384032 - 0.871307698968855*i
x16 = 4.40213281384032 + 0.871307698968855*i
x17 = 5.02264514692906 - 0.871307698968855*i
x18 = 5.02264514692906 + 0.871307698968855*i
x19 = 4.60974375664872 - 0.900273667451323*i
x20 = 4.60974375664872 + 0.900273667451323*i
x21 = 4.81503420412066 - 0.900273667451323*i
x22 = 4.81503420412066 + 0.900273667451323*i
x23 = 3.14159265358979 - 0.252344872738505*i
x24 = 0.252344872738505*i
x25 = 2.60647300082395 + 0.543070659697429*i
x26 = 2.60647300082395 - 0.543070659697429*i
x27 = 0.535119652765845 + 0.543070659697429*i
x28 = 0.535119652765845 - 0.543070659697429*i
x29 = 2.32981004578362 + 0.708304870870651*i
x30 = 2.32981004578362 - 0.708304870870651*i
x31 = 0.811782607806177 + 0.708304870870651*i
x32 = 0.811782607806177 - 0.708304870870651*i
x33 = 2.09658975731674 + 0.810160956958411*i
x34 = 2.09658975731674 - 0.810160956958411*i
x35 = 1.04500289627306 + 0.810160956958411*i
x36 = 1.04500289627306 - 0.810160956958411*i
x37 = 1.88105249333927 + 0.871307698968855*i
x38 = 1.88105249333927 - 0.871307698968855*i
x39 = 1.26054016025052 + 0.871307698968855*i
x40 = 1.26054016025052 - 0.871307698968855*i
x41 = 1.67344155053087 + 0.900273667451323*i
x42 = 1.67344155053087 - 0.900273667451323*i
x43 = 1.46815110305892 + 0.900273667451323*i
x44 = 1.46815110305892 - 0.900273667451323*i
x44 = 1.46815110305892 - 0.900273667451323*i
Уравнение 3*x^2-2*x-8=0
Уравнение 2*x^2=1/2
Уравнение x-219=370+110
Уравнение cos^22x=2