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Уравнение 3*x^2-2*x-8=0
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Уравнение 2*x^2=1/2
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Уравнение x-219=370+110
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Уравнение cos^22x=2
- Выразите {x} через y в уравнении:
- 4*x-4*y=12
- -4*x-3*y=-5
- 3*x-9*y=18
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Идентичные выражения
- cos^ два 2x=2
- косинус от в квадрате 2x равно 2
- косинус от в степени два 2x равно 2
- cos22x=2
- cos²2x=2
- cos в степени 22x=2
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Похожие выражения
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cos^22x=2 уравнение
С верным решением ты станешь самым любимым в группе❤️😊
Решение
Подробное решение
Дано уравнение
$$\cos^{22}{\left(x \right)} = 2$$
преобразуем
$$\cos^{22}{\left(x \right)} - 2 = 0$$
$$\cos^{22}{\left(x \right)} - 2 = 0$$
Сделаем замену
$$w = \cos{\left(x \right)}$$
Дано уравнение
$$w^{22} - 2 = 0$$
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:
$$\sqrt[22]{\left(1 w + 0\right)^{22}} = \sqrt[22]{2}$$
$$\sqrt[22]{\left(1 w + 0\right)^{22}} = - \sqrt[22]{2}$$
или
$$w = \sqrt[22]{2}$$
$$w = - \sqrt[22]{2}$$
Раскрываем скобочки в правой части уравнения
Получим ответ: w = 2^(1/22)
Раскрываем скобочки в правой части уравнения
Получим ответ: w = -2^(1/22)
или
$$w_{1} = - \sqrt[22]{2}$$
$$w_{2} = \sqrt[22]{2}$$
Остальные 20 корня(ей) являются комплексными.
сделаем замену:
$$z = w$$
тогда уравнение будет таким:
$$z^{22} = 2$$
Любое комплексное число можно представить так:
$$z = r e^{i p}$$
подставляем в уравнение
$$r^{22} e^{22 i p} = 2$$
где
$$r = \sqrt[22]{2}$$
- модуль комплексного числа
Подставляем r:
$$e^{22 i p} = 1$$
Используя формулу Эйлера, найдём корни для p
$$i \sin{\left(22 p \right)} + \cos{\left(22 p \right)} = 1$$
значит
$$\cos{\left(22 p \right)} = 1$$
и
$$\sin{\left(22 p \right)} = 0$$
тогда
$$p = \frac{\pi N}{11}$$
где N=0,1,2,3,...
Перебирая значения N и подставив p в формулу для z
Значит, решением будет для z:
$$z_{1} = - \sqrt[22]{2}$$
$$z_{2} = \sqrt[22]{2}$$
$$z_{3} = - \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$z_{4} = - \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$z_{5} = \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$z_{6} = \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$z_{7} = - \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$z_{8} = - \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$z_{9} = \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$z_{10} = \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$z_{11} = - \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$z_{12} = - \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$z_{13} = \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$z_{14} = \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$z_{15} = - \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$z_{16} = - \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$z_{17} = \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$z_{18} = \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$z_{19} = - \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
$$z_{20} = - \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
$$z_{21} = \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
$$z_{22} = \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
делаем обратную замену
$$z = w$$
$$w = z$$
Тогда, окончательный ответ:
$$w_{1} = - \sqrt[22]{2}$$
$$w_{2} = \sqrt[22]{2}$$
$$w_{3} = - \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$w_{4} = - \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$w_{5} = \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$w_{6} = \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$w_{7} = - \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$w_{8} = - \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$w_{9} = \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$w_{10} = \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$w_{11} = - \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$w_{12} = - \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$w_{13} = \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$w_{14} = \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$w_{15} = - \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$w_{16} = - \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$w_{17} = \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$w_{18} = \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$w_{19} = - \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
$$w_{20} = - \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
$$w_{21} = \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
$$w_{22} = \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
делаем обратную замену
$$\cos{\left(x \right)} = w$$
$$\cos{\left(x \right)} = w$$
- это простейшее тригонометрическое уравнение
Это уравнение преобразуется в
$$x = 2 \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = 2 \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
Или
$$x = 2 \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = 2 \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, где n - любое целое число
подставляем w:
$$x_{1} = 2 \pi n + \operatorname{acos}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{acos}{\left(\sqrt[22]{2} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{acos}{\left(\sqrt[22]{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{acos}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{acos}{\left(- \sqrt[22]{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{acos}{\left(- \sqrt[22]{2} \right)}$$
$$x_{3} = 2 \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi$$
$$x_{3} = 2 \pi n - \pi + \operatorname{acos}{\left(\sqrt[22]{2} \right)}$$
$$x_{3} = 2 \pi n - \pi + \operatorname{acos}{\left(\sqrt[22]{2} \right)}$$
$$x_{4} = 2 \pi n + \operatorname{acos}{\left(w_{2} \right)} - \pi$$
$$x_{4} = 2 \pi n - \pi + \operatorname{acos}{\left(- \sqrt[22]{2} \right)}$$
$$x_{4} = 2 \pi n - \pi + \operatorname{acos}{\left(- \sqrt[22]{2} \right)}$$
$$\cos^{22}{\left(x \right)} = 2$$
преобразуем
$$\cos^{22}{\left(x \right)} - 2 = 0$$
$$\cos^{22}{\left(x \right)} - 2 = 0$$
Сделаем замену
$$w = \cos{\left(x \right)}$$
Дано уравнение
$$w^{22} - 2 = 0$$
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:
$$\sqrt[22]{\left(1 w + 0\right)^{22}} = \sqrt[22]{2}$$
$$\sqrt[22]{\left(1 w + 0\right)^{22}} = - \sqrt[22]{2}$$
или
$$w = \sqrt[22]{2}$$
$$w = - \sqrt[22]{2}$$
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
$$w_{1} = - \sqrt[22]{2}$$
$$w_{2} = \sqrt[22]{2}$$
Остальные 20 корня(ей) являются комплексными.
сделаем замену:
$$z = w$$
тогда уравнение будет таким:
$$z^{22} = 2$$
Любое комплексное число можно представить так:
$$z = r e^{i p}$$
подставляем в уравнение
$$r^{22} e^{22 i p} = 2$$
где
$$r = \sqrt[22]{2}$$
- модуль комплексного числа
Подставляем r:
$$e^{22 i p} = 1$$
Используя формулу Эйлера, найдём корни для p
$$i \sin{\left(22 p \right)} + \cos{\left(22 p \right)} = 1$$
значит
$$\cos{\left(22 p \right)} = 1$$
и
$$\sin{\left(22 p \right)} = 0$$
тогда
$$p = \frac{\pi N}{11}$$
где N=0,1,2,3,...
Перебирая значения N и подставив p в формулу для z
Значит, решением будет для z:
$$z_{1} = - \sqrt[22]{2}$$
$$z_{2} = \sqrt[22]{2}$$
$$z_{3} = - \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$z_{4} = - \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$z_{5} = \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$z_{6} = \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$z_{7} = - \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$z_{8} = - \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$z_{9} = \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$z_{10} = \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$z_{11} = - \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$z_{12} = - \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$z_{13} = \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$z_{14} = \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$z_{15} = - \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$z_{16} = - \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$z_{17} = \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$z_{18} = \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$z_{19} = - \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
$$z_{20} = - \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
$$z_{21} = \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
$$z_{22} = \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
делаем обратную замену
$$z = w$$
$$w = z$$
Тогда, окончательный ответ:
$$w_{1} = - \sqrt[22]{2}$$
$$w_{2} = \sqrt[22]{2}$$
$$w_{3} = - \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$w_{4} = - \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$w_{5} = \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$w_{6} = \sqrt[22]{2} \cos{\left(\frac{\pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{\pi}{11} \right)}$$
$$w_{7} = - \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$w_{8} = - \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$w_{9} = \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$w_{10} = \sqrt[22]{2} \cos{\left(\frac{2 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{2 \pi}{11} \right)}$$
$$w_{11} = - \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$w_{12} = - \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$w_{13} = \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$w_{14} = \sqrt[22]{2} \cos{\left(\frac{3 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{3 \pi}{11} \right)}$$
$$w_{15} = - \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$w_{16} = - \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$w_{17} = \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$w_{18} = \sqrt[22]{2} \cos{\left(\frac{4 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{4 \pi}{11} \right)}$$
$$w_{19} = - \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
$$w_{20} = - \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
$$w_{21} = \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} - \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
$$w_{22} = \sqrt[22]{2} \cos{\left(\frac{5 \pi}{11} \right)} + \sqrt[22]{2} i \sin{\left(\frac{5 \pi}{11} \right)}$$
делаем обратную замену
$$\cos{\left(x \right)} = w$$
$$\cos{\left(x \right)} = w$$
- это простейшее тригонометрическое уравнение
Это уравнение преобразуется в
$$x = 2 \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = 2 \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
Или
$$x = 2 \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = 2 \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, где n - любое целое число
подставляем w:
$$x_{1} = 2 \pi n + \operatorname{acos}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{acos}{\left(\sqrt[22]{2} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{acos}{\left(\sqrt[22]{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{acos}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{acos}{\left(- \sqrt[22]{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{acos}{\left(- \sqrt[22]{2} \right)}$$
$$x_{3} = 2 \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi$$
$$x_{3} = 2 \pi n - \pi + \operatorname{acos}{\left(\sqrt[22]{2} \right)}$$
$$x_{3} = 2 \pi n - \pi + \operatorname{acos}{\left(\sqrt[22]{2} \right)}$$
$$x_{4} = 2 \pi n + \operatorname{acos}{\left(w_{2} \right)} - \pi$$
$$x_{4} = 2 \pi n - \pi + \operatorname{acos}{\left(- \sqrt[22]{2} \right)}$$
$$x_{4} = 2 \pi n - \pi + \operatorname{acos}{\left(- \sqrt[22]{2} \right)}$$
Быстрый ответ
[src]
/ / 22___\\ / / 22___\\ x_1 = - re\acos\-\/ 2 // + 2*pi - I*im\acos\-\/ 2 //
$$x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \right)}\right)}$$
/ /22___\\ x_2 = 2*pi - I*im\acos\\/ 2 //
$$x_{2} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \right)}\right)}$$
/ / 11____ 22___\\ / / 11____ 22___\\ x_3 = - re\acos\-\/ -1 *\/ 2 // + 2*pi - I*im\acos\-\/ -1 *\/ 2 //
$$x_{3} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 9/22 22___\\ 3*pi / / 9/22 22___\\
x_4 = - im\asinh\(-1) *\/ 2 // + ---- + I*re\asinh\(-1) *\/ 2 //
2
$$x_{4} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
3*pi / / 9/22 22___\\ / / 9/22 22___\\
x_5 = ---- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
$$x_{5} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ /11____ 22___\\ / /11____ 22___\\ x_6 = - re\acos\\/ -1 *\/ 2 // + 2*pi - I*im\acos\\/ -1 *\/ 2 //
$$x_{6} = - \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 2/11 22___\\ / / 2/11 22___\\ x_7 = - re\acos\-(-1) *\/ 2 // + 2*pi - I*im\acos\-(-1) *\/ 2 //
$$x_{7} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 7/22 22___\\ 3*pi / / 7/22 22___\\
x_8 = - im\asinh\(-1) *\/ 2 // + ---- + I*re\asinh\(-1) *\/ 2 //
2
$$x_{8} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
3*pi / / 7/22 22___\\ / / 7/22 22___\\
x_9 = ---- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
$$x_{9} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 2/11 22___\\ / / 2/11 22___\\ x_10 = - re\acos\(-1) *\/ 2 // + 2*pi - I*im\acos\(-1) *\/ 2 //
$$x_{10} = - \operatorname{re}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 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 ////
$$x_{11} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{5 \pi}{22} \right)} + i \cos{\left(\frac{5 \pi}{22} \right)}\right) \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{5 \pi}{22} \right)} + i \cos{\left(\frac{5 \pi}{22} \right)}\right) \right)}\right)}$$
/ / 5/22 22___\\ 3*pi / / 5/22 22___\\
x_12 = - im\asinh\(-1) *\/ 2 // + ---- + I*re\asinh\(-1) *\/ 2 //
2
$$x_{12} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
3*pi / / 5/22 22___\\ / / 5/22 22___\\
x_13 = ---- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
$$x_{13} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 3/11 22___\\ / / 3/11 22___\\ x_14 = - re\acos\(-1) *\/ 2 // + 2*pi - I*im\acos\(-1) *\/ 2 //
$$x_{14} = - \operatorname{re}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{3}{11}} \cdot \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{3}{11}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 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 ////
$$x_{15} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{3 \pi}{22} \right)} + i \cos{\left(\frac{3 \pi}{22} \right)}\right) \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{3 \pi}{22} \right)} + i \cos{\left(\frac{3 \pi}{22} \right)}\right) \right)}\right)}$$
/ / 3/22 22___\\ 3*pi / / 3/22 22___\\
x_16 = - im\asinh\(-1) *\/ 2 // + ---- + I*re\asinh\(-1) *\/ 2 //
2
$$x_{16} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
3*pi / / 3/22 22___\\ / / 3/22 22___\\
x_17 = ---- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
$$x_{17} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{3 \pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 4/11 22___\\ / / 4/11 22___\\ x_18 = - re\acos\(-1) *\/ 2 // + 2*pi - I*im\acos\(-1) *\/ 2 //
$$x_{18} = - \operatorname{re}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{4}{11}} \cdot \sqrt[22]{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{4}{11}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 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////
$$x_{19} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)}$$
/ /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////
$$x_{20} = - \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(- \sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(- \sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)}$$
/ /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////
$$x_{21} = - \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} - i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} - i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)}$$
/ /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////
$$x_{22} = - \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)}$$
/ / 22___\\ / / 22___\\ x_23 = I*im\acos\-\/ 2 // + re\acos\-\/ 2 //
$$x_{23} = \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \right)}\right)}$$
/ /22___\\ x_24 = I*im\acos\\/ 2 //
$$x_{24} = i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \right)}\right)}$$
/ / 11____ 22___\\ / / 11____ 22___\\ x_25 = I*im\acos\-\/ -1 *\/ 2 // + re\acos\-\/ -1 *\/ 2 //
$$x_{25} = \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)}$$
pi / / 9/22 22___\\ / / 9/22 22___\\
x_26 = -- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
$$x_{26} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
pi / / 9/22 22___\\ / / 9/22 22___\\
x_27 = -- - im\asinh\(-1) *\/ 2 // + I*re\asinh\(-1) *\/ 2 //
2
$$x_{27} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{9}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ /11____ 22___\\ / /11____ 22___\\ x_28 = I*im\acos\\/ -1 *\/ 2 // + re\acos\\/ -1 *\/ 2 //
$$x_{28} = \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[11]{-1} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 2/11 22___\\ / / 2/11 22___\\ x_29 = I*im\acos\-(-1) *\/ 2 // + re\acos\-(-1) *\/ 2 //
$$x_{29} = \operatorname{re}{\left(\operatorname{acos}{\left(- \left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)}$$
pi / / 7/22 22___\\ / / 7/22 22___\\
x_30 = -- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
$$x_{30} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
pi / / 7/22 22___\\ / / 7/22 22___\\
x_31 = -- - im\asinh\(-1) *\/ 2 // + I*re\asinh\(-1) *\/ 2 //
2
$$x_{31} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{7}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 2/11 22___\\ / / 2/11 22___\\ x_32 = I*im\acos\(-1) *\/ 2 // + re\acos\(-1) *\/ 2 //
$$x_{32} = \operatorname{re}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{2}{11}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 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 ////
$$x_{33} = \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{5 \pi}{22} \right)} + i \cos{\left(\frac{5 \pi}{22} \right)}\right) \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{5 \pi}{22} \right)} + i \cos{\left(\frac{5 \pi}{22} \right)}\right) \right)}\right)}$$
pi / / 5/22 22___\\ / / 5/22 22___\\
x_34 = -- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
$$x_{34} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
pi / / 5/22 22___\\ / / 5/22 22___\\
x_35 = -- - im\asinh\(-1) *\/ 2 // + I*re\asinh\(-1) *\/ 2 //
2
$$x_{35} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{5}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 3/11 22___\\ / / 3/11 22___\\ x_36 = I*im\acos\(-1) *\/ 2 // + re\acos\(-1) *\/ 2 //
$$x_{36} = \operatorname{re}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{3}{11}} \cdot \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{3}{11}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 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 ////
$$x_{37} = \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{3 \pi}{22} \right)} + i \cos{\left(\frac{3 \pi}{22} \right)}\right) \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{3 \pi}{22} \right)} + i \cos{\left(\frac{3 \pi}{22} \right)}\right) \right)}\right)}$$
pi / / 3/22 22___\\ / / 3/22 22___\\
x_38 = -- - I*re\asinh\(-1) *\/ 2 // + im\asinh\(-1) *\/ 2 //
2
$$x_{38} = \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} - i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
pi / / 3/22 22___\\ / / 3/22 22___\\
x_39 = -- - im\asinh\(-1) *\/ 2 // + I*re\asinh\(-1) *\/ 2 //
2
$$x_{39} = - \operatorname{im}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)} + \frac{\pi}{2} + i \operatorname{re}{\left(\operatorname{asinh}{\left(\left(-1\right)^{\frac{3}{22}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 4/11 22___\\ / / 4/11 22___\\ x_40 = I*im\acos\(-1) *\/ 2 // + re\acos\(-1) *\/ 2 //
$$x_{40} = \operatorname{re}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{4}{11}} \cdot \sqrt[22]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\left(-1\right)^{\frac{4}{11}} \cdot \sqrt[22]{2} \right)}\right)}$$
/ / 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////
$$x_{41} = \operatorname{re}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)}$$
/ /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////
$$x_{42} = \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(- \sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(- \sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)}$$
/ /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////
$$x_{43} = \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} - i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} - i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)}$$
/ /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////
$$x_{44} = \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt[22]{2} \left(\sin{\left(\frac{\pi}{22} \right)} + i \cos{\left(\frac{\pi}{22} \right)}\right) \right)}\right)}$$
Численный ответ
[src]
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
График