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- La ecuación:
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Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
-
Ecuación x^2+4=5x
-
Ecuación x(x^2+2x+1)=6(x+1)
-
Ecuación 4x+1=-3x+15
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
-
Expresiones idénticas
- tan5(x)=-sqrt(tres)/ tres
- tangente de 5(x) es igual a menos raíz cuadrada de (3) dividir por 3
- tangente de 5(x) es igual a menos raíz cuadrada de (tres) dividir por tres
- tan5(x)=-√(3)/3
- tan5x=-sqrt3/3
- tan5(x)=-sqrt(3) dividir por 3
-
Expresiones semejantes
- tan((5*x+pi)/3)*cot(3*x)=1
- tan(5x)=t
- tan(5*x-pi/3)=sqrt(3)/1
- tan5(x)=+sqrt(3)/3
- x-atan(5*x)=0
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x-1)=x-3
- sqrt(x+6)=x
- sqrt(16-4*x)=2
- sqrt(12-x)=x
- sqrt(5/(15-x))=1
tan5(x)=-sqrt(3)/3 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___
5 -\/ 3
tan (x) = -------
3
$$\tan^{5}{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Solución detallada
Tenemos la ecuación
$$\tan^{5}{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
cambiamos
$$\tan^{5}{\left(x \right)} + \frac{\sqrt{3}}{3} = 0$$
$$\tan^{5}{\left(x \right)} - \frac{\left(-1\right) \sqrt{3}}{3} = 0$$
Sustituimos
$$w = \tan{\left(x \right)}$$
Tenemos la ecuación
$$w^{5} - \frac{\left(-1\right) \sqrt{3}}{3} = 0$$
Ya que la potencia en la ecuación es igual a = 5 - no contiene número par en el numerador, entonces
la ecuación tendrá una raíz real.
Extraigamos la raíz de potencia 5 de las dos partes de la ecuación:
Obtenemos:
$$\sqrt[5]{w^{5}} = \sqrt[5]{- \frac{\sqrt{3}}{3}}$$
o
$$w = \frac{\sqrt[10]{3} \cdot 3^{\frac{4}{5}} \cdot 3^{\frac{4}{5}} \cdot 3^{\frac{9}{10}} \cdot 3^{\frac{9}{10}} \sqrt[5]{-1} \cdot 3^{\frac{2}{5}}}{81}$$
Abrimos los paréntesis en el miembro derecho de la ecuación
Obtenemos la respuesta: w = (-1)^(1/5)*3^(9/10)/3
Las demás 4 raíces son complejas.
hacemos el cambio:
$$z = w$$
entonces la ecuación será así:
$$z^{5} = - \frac{\sqrt{3}}{3}$$
Cualquier número complejo se puede presentar que:
$$z = r e^{i p}$$
sustituimos en la ecuación
$$r^{5} e^{5 i p} = - \frac{\sqrt{3}}{3}$$
donde
$$r = \frac{3^{\frac{9}{10}}}{3}$$
- módulo del número complejo
Sustituyamos r:
$$e^{5 i p} = -1$$
Usando la fórmula de Euler hallemos las raíces para p
$$i \sin{\left(5 p \right)} + \cos{\left(5 p \right)} = -1$$
es decir
$$\cos{\left(5 p \right)} = -1$$
y
$$\sin{\left(5 p \right)} = 0$$
entonces
$$p = \frac{2 \pi N}{5} + \frac{\pi}{5}$$
donde N=0,1,2,3,...
Seleccionando los valores de N y sustituyendo p en la fórmula para z
Es decir, la solución será para z:
$$z_{1} = - \frac{3^{\frac{9}{10}}}{3}$$
$$z_{2} = \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{3}$$
$$z_{3} = - \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6}$$
$$z_{4} = \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}$$
$$z_{5} = - \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12}$$
hacemos cambio inverso
$$z = w$$
$$w = z$$
Entonces la respuesta definitiva es:
$$w_{1} = - \frac{3^{\frac{9}{10}}}{3}$$
$$w_{2} = \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{3}$$
$$w_{3} = - \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6}$$
$$w_{4} = \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}$$
$$w_{5} = - \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12}$$
hacemos cambio inverso
$$\tan{\left(x \right)} = w$$
Tenemos la ecuación
$$\tan{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{atan}{\left(w \right)}$$
O
$$x = \pi n + \operatorname{atan}{\left(w \right)}$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = \pi n + \operatorname{atan}{\left(w_{1} \right)}$$
$$x_{1} = \pi n + \operatorname{atan}{\left(\frac{\sqrt[5]{-1} \cdot 3^{\frac{9}{10}}}{3} \right)}$$
$$x_{1} = \pi n + \operatorname{atan}{\left(\frac{\sqrt[5]{-1} \cdot 3^{\frac{9}{10}}}{3} \right)}$$
$$\tan^{5}{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
cambiamos
$$\tan^{5}{\left(x \right)} + \frac{\sqrt{3}}{3} = 0$$
$$\tan^{5}{\left(x \right)} - \frac{\left(-1\right) \sqrt{3}}{3} = 0$$
Sustituimos
$$w = \tan{\left(x \right)}$$
Tenemos la ecuación
$$w^{5} - \frac{\left(-1\right) \sqrt{3}}{3} = 0$$
Ya que la potencia en la ecuación es igual a = 5 - no contiene número par en el numerador, entonces
la ecuación tendrá una raíz real.
Extraigamos la raíz de potencia 5 de las dos partes de la ecuación:
Obtenemos:
$$\sqrt[5]{w^{5}} = \sqrt[5]{- \frac{\sqrt{3}}{3}}$$
o
$$w = \frac{\sqrt[10]{3} \cdot 3^{\frac{4}{5}} \cdot 3^{\frac{4}{5}} \cdot 3^{\frac{9}{10}} \cdot 3^{\frac{9}{10}} \sqrt[5]{-1} \cdot 3^{\frac{2}{5}}}{81}$$
Abrimos los paréntesis en el miembro derecho de la ecuación
w = 3^1/10*3^4/5*3^4/5*3^9/10*3^9/10-1^1/5*3^2/5)/81
Obtenemos la respuesta: w = (-1)^(1/5)*3^(9/10)/3
Las demás 4 raíces son complejas.
hacemos el cambio:
$$z = w$$
entonces la ecuación será así:
$$z^{5} = - \frac{\sqrt{3}}{3}$$
Cualquier número complejo se puede presentar que:
$$z = r e^{i p}$$
sustituimos en la ecuación
$$r^{5} e^{5 i p} = - \frac{\sqrt{3}}{3}$$
donde
$$r = \frac{3^{\frac{9}{10}}}{3}$$
- módulo del número complejo
Sustituyamos r:
$$e^{5 i p} = -1$$
Usando la fórmula de Euler hallemos las raíces para p
$$i \sin{\left(5 p \right)} + \cos{\left(5 p \right)} = -1$$
es decir
$$\cos{\left(5 p \right)} = -1$$
y
$$\sin{\left(5 p \right)} = 0$$
entonces
$$p = \frac{2 \pi N}{5} + \frac{\pi}{5}$$
donde N=0,1,2,3,...
Seleccionando los valores de N y sustituyendo p en la fórmula para z
Es decir, la solución será para z:
$$z_{1} = - \frac{3^{\frac{9}{10}}}{3}$$
$$z_{2} = \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{3}$$
$$z_{3} = - \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6}$$
$$z_{4} = \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}$$
$$z_{5} = - \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12}$$
hacemos cambio inverso
$$z = w$$
$$w = z$$
Entonces la respuesta definitiva es:
$$w_{1} = - \frac{3^{\frac{9}{10}}}{3}$$
$$w_{2} = \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{3}$$
$$w_{3} = - \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6}$$
$$w_{4} = \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12}$$
$$w_{5} = - \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12}$$
hacemos cambio inverso
$$\tan{\left(x \right)} = w$$
Tenemos la ecuación
$$\tan{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{atan}{\left(w \right)}$$
O
$$x = \pi n + \operatorname{atan}{\left(w \right)}$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = \pi n + \operatorname{atan}{\left(w_{1} \right)}$$
$$x_{1} = \pi n + \operatorname{atan}{\left(\frac{\sqrt[5]{-1} \cdot 3^{\frac{9}{10}}}{3} \right)}$$
$$x_{1} = \pi n + \operatorname{atan}{\left(\frac{\sqrt[5]{-1} \cdot 3^{\frac{9}{10}}}{3} \right)}$$
Suma y producto de raíces
[src]
suma
/ / ___________ ___________\\ / / ___________ ___________\\ / / ___________ ___________ ___________ ___________ ___________ ___________\\ / / ___________ ___________ ___________ ___________ ___________ ___________\\ / / ___________ ___________ ___________ ___________ ___________ ___________\\ / / ___________ ___________ ___________ ___________ ___________ ___________\\ / / ___________\\ / / ___________\\
| | / ___ / ___ || | | / ___ / ___ || | | / ___ / ___ / ___ / ___ / ___ / ___ || | | / ___ / ___ / ___ / ___ / ___ / ___ || | | / ___ / ___ / ___ / ___ / ___ / ___ || | | / ___ / ___ / ___ / ___ / ___ / ___ || | | / ___ || | | / ___ ||
| | 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 || | | 9/10 / 5 \/ 5 ||
/ 9/10\ | | 9/10 9/10 ___ I*3 * / - - ----- I*3 *\/ 5 * / - - ----- || | | 9/10 9/10 ___ I*3 * / - - ----- I*3 *\/ 5 * / - - ----- || | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- || | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- || | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- || | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- || | | 9/10 9/10 ___ I*3 * / - - ----- || | | 9/10 9/10 ___ I*3 * / - - ----- ||
|3 | | | 3 3 *\/ 5 \/ 8 8 \/ 8 8 || | | 3 3 *\/ 5 \/ 8 8 \/ 8 8 || | | 3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 || | | 3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 || | |3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 || | |3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 || | |3 3 *\/ 5 \/ 8 8 || | |3 3 *\/ 5 \/ 8 8 ||
- atan|-----| + - re|atan|- ----- + ----------- + ------------------------ + ------------------------------|| - I*im|atan|- ----- + ----------- + ------------------------ + ------------------------------|| + - re|atan|- ----- - --------------------------------------- + ------------------------ + ------------------------ - ------------------------------ + ------------------------------|| - I*im|atan|- ----- - --------------------------------------- + ------------------------ + ------------------------ - ------------------------------ + ------------------------------|| + I*im|atan|----- - --------------------------------------- - ------------------------ + ------------------------ + ------------------------------ + ------------------------------|| + re|atan|----- - --------------------------------------- - ------------------------ + ------------------------ + ------------------------------ + ------------------------------|| + I*im|atan|----- + ----------- + ------------------------|| + re|atan|----- + ----------- + ------------------------||
\ 3 / \ \ 12 12 6 6 // \ \ 12 12 6 6 // \ \ 12 3 12 12 12 12 // \ \ 12 3 12 12 12 12 // \ \ 12 3 12 12 12 12 // \ \ 12 3 12 12 12 12 // \ \ 12 12 3 // \ \ 12 12 3 //
$$\left(\left(\left(- \operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{3} \right)} + \left(- \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} \right)}\right)}\right)\right) + \left(- \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} - \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} - \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{3} \right)}\right)}\right)$$
=
/ / ___________ ___________\\ / / ___________ ___________ ___________ ___________ ___________ ___________\\ / / ___________\\ / / ___________ ___________ ___________ ___________ ___________ ___________\\ / / ___________ ___________\\ / / ___________ ___________ ___________ ___________ ___________ ___________\\ / / ___________\\ / / ___________ ___________ ___________ ___________ ___________ ___________\\
| | / ___ / ___ || | | / ___ / ___ / ___ / ___ / ___ / ___ || | | / ___ || | | / ___ / ___ / ___ / ___ / ___ / ___ || | | / ___ / ___ || | | / ___ / ___ / ___ / ___ / ___ / ___ || | | / ___ || | | / ___ / ___ / ___ / ___ / ___ / ___ ||
| | 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 || | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 || | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 ||
/ 9/10\ | | 9/10 9/10 ___ I*3 * / - - ----- I*3 *\/ 5 * / - - ----- || | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- || | | 9/10 9/10 ___ I*3 * / - - ----- || | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- || | | 9/10 9/10 ___ I*3 * / - - ----- I*3 *\/ 5 * / - - ----- || | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- || | | 9/10 9/10 ___ I*3 * / - - ----- || | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- ||
|3 | | | 3 3 *\/ 5 \/ 8 8 \/ 8 8 || | | 3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 || | |3 3 *\/ 5 \/ 8 8 || | |3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 || | | 3 3 *\/ 5 \/ 8 8 \/ 8 8 || | | 3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 || | |3 3 *\/ 5 \/ 8 8 || | |3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 ||
- atan|-----| - re|atan|- ----- + ----------- + ------------------------ + ------------------------------|| - re|atan|- ----- - --------------------------------------- + ------------------------ + ------------------------ - ------------------------------ + ------------------------------|| + I*im|atan|----- + ----------- + ------------------------|| + I*im|atan|----- - --------------------------------------- - ------------------------ + ------------------------ + ------------------------------ + ------------------------------|| - I*im|atan|- ----- + ----------- + ------------------------ + ------------------------------|| - I*im|atan|- ----- - --------------------------------------- + ------------------------ + ------------------------ - ------------------------------ + ------------------------------|| + re|atan|----- + ----------- + ------------------------|| + re|atan|----- - --------------------------------------- - ------------------------ + ------------------------ + ------------------------------ + ------------------------------||
\ 3 / \ \ 12 12 6 6 // \ \ 12 3 12 12 12 12 // \ \ 12 12 3 // \ \ 12 3 12 12 12 12 // \ \ 12 12 6 6 // \ \ 12 3 12 12 12 12 // \ \ 12 12 3 // \ \ 12 3 12 12 12 12 //
$$- \operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{3} \right)} - \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} \right)}\right)} + \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)} - \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} - \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)} + \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} - \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)}$$
producto
/ / / ___________ ___________\\ / / ___________ ___________\\\ / / / ___________ ___________ ___________ ___________ ___________ ___________\\ / / ___________ ___________ ___________ ___________ ___________ ___________\\\ / / / ___________ ___________ ___________ ___________ ___________ ___________\\ / / ___________ ___________ ___________ ___________ ___________ ___________\\\ / / / ___________\\ / / ___________\\\
| | | / ___ / ___ || | | / ___ / ___ ||| | | | / ___ / ___ / ___ / ___ / ___ / ___ || | | / ___ / ___ / ___ / ___ / ___ / ___ ||| | | | / ___ / ___ / ___ / ___ / ___ / ___ || | | / ___ / ___ / ___ / ___ / ___ / ___ ||| | | | / ___ || | | / ___ |||
| | | 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 ||| | | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 ||| | | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 ||| | | | 9/10 / 5 \/ 5 || | | 9/10 / 5 \/ 5 |||
/ 9/10\ | | | 9/10 9/10 ___ I*3 * / - - ----- I*3 *\/ 5 * / - - ----- || | | 9/10 9/10 ___ I*3 * / - - ----- I*3 *\/ 5 * / - - ----- ||| | | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- || | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- ||| | | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- || | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- ||| | | | 9/10 9/10 ___ I*3 * / - - ----- || | | 9/10 9/10 ___ I*3 * / - - ----- |||
|3 | | | | 3 3 *\/ 5 \/ 8 8 \/ 8 8 || | | 3 3 *\/ 5 \/ 8 8 \/ 8 8 ||| | | | 3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 || | | 3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 ||| | | |3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 || | |3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 ||| | | |3 3 *\/ 5 \/ 8 8 || | |3 3 *\/ 5 \/ 8 8 |||
-atan|-----|*|- re|atan|- ----- + ----------- + ------------------------ + ------------------------------|| - I*im|atan|- ----- + ----------- + ------------------------ + ------------------------------|||*|- re|atan|- ----- - --------------------------------------- + ------------------------ + ------------------------ - ------------------------------ + ------------------------------|| - I*im|atan|- ----- - --------------------------------------- + ------------------------ + ------------------------ - ------------------------------ + ------------------------------|||*|I*im|atan|----- - --------------------------------------- - ------------------------ + ------------------------ + ------------------------------ + ------------------------------|| + re|atan|----- - --------------------------------------- - ------------------------ + ------------------------ + ------------------------------ + ------------------------------|||*|I*im|atan|----- + ----------- + ------------------------|| + re|atan|----- + ----------- + ------------------------|||
\ 3 / \ \ \ 12 12 6 6 // \ \ 12 12 6 6 /// \ \ \ 12 3 12 12 12 12 // \ \ 12 3 12 12 12 12 /// \ \ \ 12 3 12 12 12 12 // \ \ 12 3 12 12 12 12 /// \ \ \ 12 12 3 // \ \ 12 12 3 ///
$$\left(- \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} \right)}\right)}\right) \left(- \operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{3} \right)}\right) \left(- \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} - \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} - \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{3} \right)}\right)}\right)$$
=
/ / / / ___________\\\ / / / ___________\\\\ / / / / ___________ ___________\\\ / / / ___________ ___________\\\\ / / / / ___________ ___________ ___________ ___________\\\ / / / ___________ ___________ ___________ ___________\\\\ / / / / ___________ ___________ ___________ ___________\\\ / / / ___________ ___________ ___________ ___________\\\\ | | | 9/10 | ___ ___ / ___ ||| | | 9/10 | ___ ___ / ___ |||| | | | 9/10 | ___ ___ / ___ ____ / ___ ||| | | 9/10 | ___ ___ / ___ ____ / ___ |||| | | | 9/10 | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ ||| | | 9/10 | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ |||| | | | 9/10 | ___ ___ / ___ ____ / ___ ____ / ___ ___ / ___ ||| | | 9/10 | ___ ___ / ___ ____ / ___ ____ / ___ ___ / ___ |||| / 9/10\ | | |3 *\1 + \/ 5 + I*\/ 2 *\/ 5 - \/ 5 /|| | |3 *\1 + \/ 5 + I*\/ 2 *\/ 5 - \/ 5 /||| | | |3 *\-2 + 2*\/ 5 + I*\/ 2 *\/ 5 - \/ 5 + I*\/ 10 *\/ 5 - \/ 5 /|| | |3 *\-2 + 2*\/ 5 + I*\/ 2 *\/ 5 - \/ 5 + I*\/ 10 *\/ 5 - \/ 5 /||| | | |3 *\-4 - 4*\/ 5 + I*\/ 2 *\/ 5 + \/ 5 + I*\/ 2 *\/ 5 - \/ 5 + I*\/ 10 *\/ 5 + \/ 5 - I*\/ 10 *\/ 5 - \/ 5 /|| | |3 *\-4 - 4*\/ 5 + I*\/ 2 *\/ 5 + \/ 5 + I*\/ 2 *\/ 5 - \/ 5 + I*\/ 10 *\/ 5 + \/ 5 - I*\/ 10 *\/ 5 - \/ 5 /||| | | |3 *\4 - 4*\/ 5 + I*\/ 2 *\/ 5 + \/ 5 + I*\/ 10 *\/ 5 + \/ 5 + I*\/ 10 *\/ 5 - \/ 5 - I*\/ 2 *\/ 5 - \/ 5 /|| | |3 *\4 - 4*\/ 5 + I*\/ 2 *\/ 5 + \/ 5 + I*\/ 10 *\/ 5 + \/ 5 + I*\/ 10 *\/ 5 - \/ 5 - I*\/ 2 *\/ 5 - \/ 5 /||| |3 | -|I*im|atan|------------------------------------------|| + re|atan|------------------------------------------|||*|I*im|atan|-----------------------------------------------------------------------|| + re|atan|-----------------------------------------------------------------------|||*|I*im|atan|--------------------------------------------------------------------------------------------------------------------------|| + re|atan|--------------------------------------------------------------------------------------------------------------------------|||*|I*im|atan|-------------------------------------------------------------------------------------------------------------------------|| + re|atan|-------------------------------------------------------------------------------------------------------------------------|||*atan|-----| \ \ \ 12 // \ \ 12 /// \ \ \ 24 // \ \ 24 /// \ \ \ 48 // \ \ 48 /// \ \ \ 48 // \ \ 48 /// \ 3 /
$$- \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}} \left(1 + \sqrt{5} + \sqrt{2} i \sqrt{5 - \sqrt{5}}\right)}{12} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}} \left(1 + \sqrt{5} + \sqrt{2} i \sqrt{5 - \sqrt{5}}\right)}{12} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}} \left(-2 + 2 \sqrt{5} + \sqrt{2} i \sqrt{5 - \sqrt{5}} + \sqrt{10} i \sqrt{5 - \sqrt{5}}\right)}{24} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}} \left(-2 + 2 \sqrt{5} + \sqrt{2} i \sqrt{5 - \sqrt{5}} + \sqrt{10} i \sqrt{5 - \sqrt{5}}\right)}{24} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}} \left(- 4 \sqrt{5} - 4 - \sqrt{10} i \sqrt{5 - \sqrt{5}} + \sqrt{2} i \sqrt{5 - \sqrt{5}} + \sqrt{2} i \sqrt{\sqrt{5} + 5} + \sqrt{10} i \sqrt{\sqrt{5} + 5}\right)}{48} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}} \left(- 4 \sqrt{5} - 4 - \sqrt{10} i \sqrt{5 - \sqrt{5}} + \sqrt{2} i \sqrt{5 - \sqrt{5}} + \sqrt{2} i \sqrt{\sqrt{5} + 5} + \sqrt{10} i \sqrt{\sqrt{5} + 5}\right)}{48} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}} \left(- 4 \sqrt{5} + 4 - \sqrt{2} i \sqrt{5 - \sqrt{5}} + \sqrt{2} i \sqrt{\sqrt{5} + 5} + \sqrt{10} i \sqrt{5 - \sqrt{5}} + \sqrt{10} i \sqrt{\sqrt{5} + 5}\right)}{48} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}} \left(- 4 \sqrt{5} + 4 - \sqrt{2} i \sqrt{5 - \sqrt{5}} + \sqrt{2} i \sqrt{\sqrt{5} + 5} + \sqrt{10} i \sqrt{5 - \sqrt{5}} + \sqrt{10} i \sqrt{\sqrt{5} + 5}\right)}{48} \right)}\right)}\right) \operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{3} \right)}$$
-(i*im(atan(3^(9/10)*(1 + sqrt(5) + i*sqrt(2)*sqrt(5 - sqrt(5)))/12)) + re(atan(3^(9/10)*(1 + sqrt(5) + i*sqrt(2)*sqrt(5 - sqrt(5)))/12)))*(i*im(atan(3^(9/10)*(-2 + 2*sqrt(5) + i*sqrt(2)*sqrt(5 - sqrt(5)) + i*sqrt(10)*sqrt(5 - sqrt(5)))/24)) + re(atan(3^(9/10)*(-2 + 2*sqrt(5) + i*sqrt(2)*sqrt(5 - sqrt(5)) + i*sqrt(10)*sqrt(5 - sqrt(5)))/24)))*(i*im(atan(3^(9/10)*(-4 - 4*sqrt(5) + i*sqrt(2)*sqrt(5 + sqrt(5)) + i*sqrt(2)*sqrt(5 - sqrt(5)) + i*sqrt(10)*sqrt(5 + sqrt(5)) - i*sqrt(10)*sqrt(5 - sqrt(5)))/48)) + re(atan(3^(9/10)*(-4 - 4*sqrt(5) + i*sqrt(2)*sqrt(5 + sqrt(5)) + i*sqrt(2)*sqrt(5 - sqrt(5)) + i*sqrt(10)*sqrt(5 + sqrt(5)) - i*sqrt(10)*sqrt(5 - sqrt(5)))/48)))*(i*im(atan(3^(9/10)*(4 - 4*sqrt(5) + i*sqrt(2)*sqrt(5 + sqrt(5)) + i*sqrt(10)*sqrt(5 + sqrt(5)) + i*sqrt(10)*sqrt(5 - sqrt(5)) - i*sqrt(2)*sqrt(5 - sqrt(5)))/48)) + re(atan(3^(9/10)*(4 - 4*sqrt(5) + i*sqrt(2)*sqrt(5 + sqrt(5)) + i*sqrt(10)*sqrt(5 + sqrt(5)) + i*sqrt(10)*sqrt(5 - sqrt(5)) - i*sqrt(2)*sqrt(5 - sqrt(5)))/48)))*atan(3^(9/10)/3)
Respuesta rápida
[src]
/ 9/10\
|3 |
x1 = -atan|-----|
\ 3 /
$$x_{1} = - \operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{3} \right)}$$
/ / ___________ ___________\\ / / ___________ ___________\\
| | / ___ / ___ || | | / ___ / ___ ||
| | 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 ||
| | 9/10 9/10 ___ I*3 * / - - ----- I*3 *\/ 5 * / - - ----- || | | 9/10 9/10 ___ I*3 * / - - ----- I*3 *\/ 5 * / - - ----- ||
| | 3 3 *\/ 5 \/ 8 8 \/ 8 8 || | | 3 3 *\/ 5 \/ 8 8 \/ 8 8 ||
x2 = - re|atan|- ----- + ----------- + ------------------------ + ------------------------------|| - I*im|atan|- ----- + ----------- + ------------------------ + ------------------------------||
\ \ 12 12 6 6 // \ \ 12 12 6 6 //
$$x_{2} = - \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{6} \right)}\right)}$$
/ / ___________ ___________ ___________ ___________ ___________ ___________\\ / / ___________ ___________ ___________ ___________ ___________ ___________\\
| | / ___ / ___ / ___ / ___ / ___ / ___ || | | / ___ / ___ / ___ / ___ / ___ / ___ ||
| | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 ||
| | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- || | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- ||
| | 3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 || | | 3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 ||
x3 = - re|atan|- ----- - --------------------------------------- + ------------------------ + ------------------------ - ------------------------------ + ------------------------------|| - I*im|atan|- ----- - --------------------------------------- + ------------------------ + ------------------------ - ------------------------------ + ------------------------------||
\ \ 12 3 12 12 12 12 // \ \ 12 3 12 12 12 12 //
$$x_{3} = - \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} - \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} - \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)}$$
/ / ___________ ___________ ___________ ___________ ___________ ___________\\ / / ___________ ___________ ___________ ___________ ___________ ___________\\
| | / ___ / ___ / ___ / ___ / ___ / ___ || | | / ___ / ___ / ___ / ___ / ___ / ___ ||
| | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 || | | 9/10 / 5 \/ 5 / 5 \/ 5 9/10 / 5 \/ 5 9/10 / 5 \/ 5 9/10 ___ / 5 \/ 5 9/10 ___ / 5 \/ 5 ||
| | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- || | | 9/10 3 * / - - ----- * / - + ----- I*3 * / - - ----- I*3 * / - + ----- I*3 *\/ 5 * / - - ----- I*3 *\/ 5 * / - + ----- ||
| |3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 || | |3 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 ||
x4 = I*im|atan|----- - --------------------------------------- - ------------------------ + ------------------------ + ------------------------------ + ------------------------------|| + re|atan|----- - --------------------------------------- - ------------------------ + ------------------------ + ------------------------------ + ------------------------------||
\ \ 12 3 12 12 12 12 // \ \ 12 3 12 12 12 12 //
$$x_{4} = \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3^{\frac{9}{10}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{3} + \frac{3^{\frac{9}{10}}}{12} - \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{12} \right)}\right)}$$
/ / ___________\\ / / ___________\\
| | / ___ || | | / ___ ||
| | 9/10 / 5 \/ 5 || | | 9/10 / 5 \/ 5 ||
| | 9/10 9/10 ___ I*3 * / - - ----- || | | 9/10 9/10 ___ I*3 * / - - ----- ||
| |3 3 *\/ 5 \/ 8 8 || | |3 3 *\/ 5 \/ 8 8 ||
x5 = I*im|atan|----- + ----------- + ------------------------|| + re|atan|----- + ----------- + ------------------------||
\ \ 12 12 3 // \ \ 12 12 3 //
$$x_{5} = \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{9}{10}}}{12} + \frac{3^{\frac{9}{10}} \sqrt{5}}{12} + \frac{3^{\frac{9}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{3} \right)}\right)}$$
x5 = re(atan(3^(9/10)/12 + 3^(9/10)*sqrt(5)/12 + 3^(9/10)*i*sqrt(5/8 - sqrt(5)/8)/3)) + i*im(atan(3^(9/10)/12 + 3^(9/10)*sqrt(5)/12 + 3^(9/10)*i*sqrt(5/8 - sqrt(5)/8)/3))
Respuesta numérica
[src]
x1 = -305.46506511234
x2 = -66.7040234395157
x3 = 18.1189782074087
x4 = -101.261542629003
x5 = 68.3844606648454
x6 = 40.1101267825373
x7 = -22.7217262892586
x8 = -69.8456160931055
x9 = -85.5535793610544
x10 = -10848.6500105597
x11 = -123.252691204132
x12 = 58.9596827040761
x13 = -35.2880969036177
x14 = -899.226076640811
x15 = 14.9773855538189
x16 = 52.6764973968965
x17 = 90.375609239974
x18 = 46.3933120897169
x19 = -32.146504250028
x20 = -79.2703940538749
x21 = -33625.1967490857
x22 = -25.8633189428484
x23 = -13.2969483284892
x24 = 178322.35162535
x25 = 84.0924239327944
x26 = -468.827883099009
x27 = -5297621.29843638
x28 = -11447607863.8933
x29 = 17931.4802889764
x30 = -1569405.33182707
x31 = -3.87217036771981
x32 = 43.2517194361271
x33 = -3396.7922362447
x34 = -47.8544675179769
x35 = 62.1012753576658
x36 = 24.4021635145883
x37 = 30.6853488217679
x38 = -7.01376302130961
x39 = -19.5801336356688
x40 = -57.2792454787463
x41 = 96.6587945471536
x42 = 2.41101493945977
x43 = -63.5624307859259
x44 = 36.9685341289475
x45 = 39187.4961831649
x46 = 8.69420024663936
x47 = 74.667645972025
x48 = -955.774744405427
x49 = -91.836764668234
x50 = 3480.15408246336
x51 = -41.5712822107973
x52 = -44.7128748643871
x53 = 80.9508312792046
x53 = 80.9508312792046