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Ecuación x^6=-3
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Ecuación 4x+3=-2x
- Ecuación (1/5)*x*(5*x*-4*x+3)=0
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- Factorizar el polinomio:
- x^2+y^2
- Forma canónica:
- x^2+y^2
- Límite de la función:
- x^2+y^2
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Expresiones idénticas
- x^ dos +y^ dos = dieciséis *cos(pi*t/ tres)^(dos)+ nueve *sin(pi*t/ tres)^(dos)
- x al cuadrado más y al cuadrado es igual a 16 multiplicar por coseno de ( número pi multiplicar por t dividir por 3) en el grado (2) más 9 multiplicar por seno de ( número pi multiplicar por t dividir por 3) en el grado (2)
- x en el grado dos más y en el grado dos es igual a dieciséis multiplicar por coseno de ( número pi multiplicar por t dividir por tres) en el grado (dos) más nueve multiplicar por seno de ( número pi multiplicar por t dividir por tres) en el grado (dos)
- x2+y2=16*cos(pi*t/3)(2)+9*sin(pi*t/3)(2)
- x2+y2=16*cospi*t/32+9*sinpi*t/32
- x²+y²=16*cos(pi*t/3)^(2)+9*sin(pi*t/3)^(2)
- x en el grado 2+y en el grado 2=16*cos(pi*t/3) en el grado (2)+9*sin(pi*t/3) en el grado (2)
- x^2+y^2=16cos(pit/3)^(2)+9sin(pit/3)^(2)
- x2+y2=16cos(pit/3)(2)+9sin(pit/3)(2)
- x2+y2=16cospit/32+9sinpit/32
- x^2+y^2=16cospit/3^2+9sinpit/3^2
- x^2+y^2=16*cos(pi*t dividir por 3)^(2)+9*sin(pi*t dividir por 3)^(2)
-
Expresiones semejantes
- x^2-y^2=16*cos(pi*t/3)^(2)+9*sin(pi*t/3)^(2)
- x^2+y^2=16*cos(pi*t/3)^(2)-9*sin(pi*t/3)^(2)
x^2+y^2=16*cos(pi*t/3)^(2)+9*sin(pi*t/3)^(2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 2/pi*t\ 2/pi*t\
x + y = 16*cos |----| + 9*sin |----|
\ 3 / \ 3 /
$$x^{2} + y^{2} = 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} + 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$x^{2} + y^{2} = 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} + 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}$$
en
$$\left(x^{2} + y^{2}\right) + \left(- 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} - 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}\right) = 0$$
Abramos la expresión en la ecuación
$$\left(x^{2} + y^{2}\right) + \left(- 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} - 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}\right) = 0$$
Obtenemos la ecuación cuadrática
$$x^{2} + y^{2} - 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} - 16 \cos^{2}{\left(\frac{\pi t}{3} \right)} = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 1$$
$$b = 0$$
$$c = y^{2} - 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} - 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{\sqrt{- 4 y^{2} + 36 \sin^{2}{\left(\frac{\pi t}{3} \right)} + 64 \cos^{2}{\left(\frac{\pi t}{3} \right)}}}{2}$$
$$x_{2} = - \frac{\sqrt{- 4 y^{2} + 36 \sin^{2}{\left(\frac{\pi t}{3} \right)} + 64 \cos^{2}{\left(\frac{\pi t}{3} \right)}}}{2}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$x^{2} + y^{2} = 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} + 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}$$
en
$$\left(x^{2} + y^{2}\right) + \left(- 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} - 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}\right) = 0$$
Abramos la expresión en la ecuación
$$\left(x^{2} + y^{2}\right) + \left(- 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} - 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}\right) = 0$$
Obtenemos la ecuación cuadrática
$$x^{2} + y^{2} - 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} - 16 \cos^{2}{\left(\frac{\pi t}{3} \right)} = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 1$$
$$b = 0$$
$$c = y^{2} - 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} - 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (y^2 - 16*cos(pi*t/3)^2 - 9*sin(pi*t/3)^2) = -4*y^2 + 36*sin(pi*t/3)^2 + 64*cos(pi*t/3)^2
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{\sqrt{- 4 y^{2} + 36 \sin^{2}{\left(\frac{\pi t}{3} \right)} + 64 \cos^{2}{\left(\frac{\pi t}{3} \right)}}}{2}$$
$$x_{2} = - \frac{\sqrt{- 4 y^{2} + 36 \sin^{2}{\left(\frac{\pi t}{3} \right)} + 64 \cos^{2}{\left(\frac{\pi t}{3} \right)}}}{2}$$
Teorema de Cardano-Vieta
es ecuación cuadrática reducida
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = y^{2} - 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} - 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = y^{2} - 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} - 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = y^{2} - 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} - 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = y^{2} - 9 \sin^{2}{\left(\frac{\pi t}{3} \right)} - 16 \cos^{2}{\left(\frac{\pi t}{3} \right)}$$
Gráfica
Respuesta rápida
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__________________________________________________________________________________________________________________________________________________________________________________ / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\ 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\\ __________________________________________________________________________________________________________________________________________________________________________________ / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\ 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\\
/ 2 2 |atan2|-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------||| / 2 2 |atan2|-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|||
/ / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | \ \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 //| / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | \ \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 //|
x1 = - 4 / |-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *cos|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I*4 / |-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *sin|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\/ \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ 2 / \/ \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ 2 /
$$x_{1} = - i \sqrt[4]{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)} - \sqrt[4]{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)}$$
__________________________________________________________________________________________________________________________________________________________________________________ / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\ 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\\ __________________________________________________________________________________________________________________________________________________________________________________ / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\ 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\\
/ 2 2 |atan2|-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------||| / 2 2 |atan2|-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|||
/ / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | \ \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 //| / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | \ \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 //|
x2 = 4 / |-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *cos|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*4 / |-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *sin|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\/ \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ 2 / \/ \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ 2 /
$$x_{2} = i \sqrt[4]{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)} + \sqrt[4]{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)}$$
x2 = i*((-14*sin(pi*re(t)/3)*cos(pi*re(t)/3)*sinh(pi*im(t)/3)*cosh(pi*im(t)/3) - 2*re(y)*im(y))^2 + (-7*sin(pi*re(t)/3)^2*cosh(pi*im(t)/3)^2 + 7*cos(pi*re(t)/3)^2*sinh(pi*im(t)/3)^2 - re(y)^2 + im(y)^2 + 16)^2)^(1/4)*sin(atan2(-14*sin(pi*re(t)/3)*cos(pi*re(t)/3)*sinh(pi*im(t)/3)*cosh(pi*im(t)/3) - 2*re(y)*im(y, -7*sin(pi*re(t)/3)^2*cosh(pi*im(t)/3)^2 + 7*cos(pi*re(t)/3)^2*sinh(pi*im(t)/3)^2 - re(y)^2 + im(y)^2 + 16)/2) + ((-14*sin(pi*re(t)/3)*cos(pi*re(t)/3)*sinh(pi*im(t)/3)*cosh(pi*im(t)/3) - 2*re(y)*im(y))^2 + (-7*sin(pi*re(t)/3)^2*cosh(pi*im(t)/3)^2 + 7*cos(pi*re(t)/3)^2*sinh(pi*im(t)/3)^2 - re(y)^2 + im(y)^2 + 16)^2)^(1/4)*cos(atan2(-14*sin(pi*re(t)/3)*cos(pi*re(t)/3)*sinh(pi*im(t)/3)*cosh(pi*im(t)/3) - 2*re(y)*im(y), -7*sin(pi*re(t)/3)^2*cosh(pi*im(t)/3)^2 + 7*cos(pi*re(t)/3)^2*sinh(pi*im(t)/3)^2 - re(y)^2 + im(y)^2 + 16)/2))
Suma y producto de raíces
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suma
__________________________________________________________________________________________________________________________________________________________________________________ / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\ 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\\ __________________________________________________________________________________________________________________________________________________________________________________ / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\ 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\\ __________________________________________________________________________________________________________________________________________________________________________________ / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\ 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\\ __________________________________________________________________________________________________________________________________________________________________________________ / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\ 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\\
/ 2 2 |atan2|-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------||| / 2 2 |atan2|-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------||| / 2 2 |atan2|-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------||| / 2 2 |atan2|-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|||
/ / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | \ \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 //| / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | \ \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 //| / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | \ \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 //| / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | \ \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 //|
- 4 / |-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *cos|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I*4 / |-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *sin|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + 4 / |-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *cos|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*4 / |-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *sin|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\/ \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ 2 / \/ \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ 2 / \/ \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ 2 / \/ \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ 2 /
$$\left(- i \sqrt[4]{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)} - \sqrt[4]{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)} + \sqrt[4]{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ __________________________________________________________________________________________________________________________________________________________________________________ / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\ 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\\ __________________________________________________________________________________________________________________________________________________________________________________ / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\ 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\\\ / __________________________________________________________________________________________________________________________________________________________________________________ / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\ 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\\ __________________________________________________________________________________________________________________________________________________________________________________ / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\ 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\\\ | / 2 2 |atan2|-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------||| / 2 2 |atan2|-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|||| | / 2 2 |atan2|-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------||| / 2 2 |atan2|-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|||| | / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | \ \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 //| / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | \ \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 //|| | / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | \ \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 //| / / /pi*re(t)\ /pi*im(t)\ /pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | \ \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 //|| |- 4 / |-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *cos|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I*4 / |-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *sin|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||*|4 / |-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *cos|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*4 / |-2*im(y)*re(y) - 14*cos|--------|*cosh|--------|*sin|--------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *sin|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| \ \/ \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ 2 / \/ \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ 2 // \\/ \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ 2 / \/ \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ 2 //
$$\left(- i \sqrt[4]{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)} - \sqrt[4]{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)} + \sqrt[4]{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 14 \sin{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cos{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)}\right)$$
=
2
/ / / /2*pi*re(t)\ /2*pi*im(t)\ \\ / / /2*pi*re(t)\ /2*pi*im(t)\ \\\
| | | 7*sin|----------|*sinh|----------| || | | 7*sin|----------|*sinh|----------| |||
____________________________________________________________________________________________________________________________________________________________________ | | | \ 3 / \ 3 / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\|| | | \ 3 / \ 3 / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\|||
/ 2 2 | |atan2|-2*im(y)*re(y) - ----------------------------------, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------||| |atan2|-2*im(y)*re(y) - ----------------------------------, 16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------||||
/ / /pi*im(t)\ /2*pi*re(t)\ /pi*im(t)\\ / 2 2 2/pi*im(t)\ 2/pi*re(t)\ 2/pi*re(t)\ 2/pi*im(t)\\ | | \ 2 \ 3 / \ 3 / \ 3 / \ 3 //| | \ 2 \ 3 / \ 3 / \ 3 / \ 3 //||
- / |2*im(y)*re(y) + 7*cosh|--------|*sin|----------|*sinh|--------|| + |16 + im (y) - re (y) - 7*cosh |--------|*sin |--------| + 7*cos |--------|*sinh |--------|| *|I*sin|------------------------------------------------------------------------------------------------------------------------------------------------------| + cos|------------------------------------------------------------------------------------------------------------------------------------------------------||
\/ \ \ 3 / \ 3 / \ 3 // \ \ 3 / \ 3 / \ 3 / \ 3 // \ \ 2 / \ 2 //
$$- \left(i \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{7 \sin{\left(\frac{2 \pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{2 \pi \operatorname{im}{\left(t\right)}}{3} \right)}}{2} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)} + \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{7 \sin{\left(\frac{2 \pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{2 \pi \operatorname{im}{\left(t\right)}}{3} \right)}}{2} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16 \right)}}{2} \right)}\right)^{2} \sqrt{\left(7 \sin{\left(\frac{2 \pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} \cosh{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 7 \sin^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \cosh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} + 7 \cos^{2}{\left(\frac{\pi \operatorname{re}{\left(t\right)}}{3} \right)} \sinh^{2}{\left(\frac{\pi \operatorname{im}{\left(t\right)}}{3} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 16\right)^{2}}$$
-sqrt((2*im(y)*re(y) + 7*cosh(pi*im(t)/3)*sin(2*pi*re(t)/3)*sinh(pi*im(t)/3))^2 + (16 + im(y)^2 - re(y)^2 - 7*cosh(pi*im(t)/3)^2*sin(pi*re(t)/3)^2 + 7*cos(pi*re(t)/3)^2*sinh(pi*im(t)/3)^2)^2)*(i*sin(atan2(-2*im(y)*re(y) - 7*sin(2*pi*re(t)/3)*sinh(2*pi*im(t)/3)/2, 16 + im(y)^2 - re(y)^2 - 7*cosh(pi*im(t)/3)^2*sin(pi*re(t)/3)^2 + 7*cos(pi*re(t)/3)^2*sinh(pi*im(t)/3)^2)/2) + cos(atan2(-2*im(y)*re(y) - 7*sin(2*pi*re(t)/3)*sinh(2*pi*im(t)/3)/2, 16 + im(y)^2 - re(y)^2 - 7*cosh(pi*im(t)/3)^2*sin(pi*re(t)/3)^2 + 7*cos(pi*re(t)/3)^2*sinh(pi*im(t)/3)^2)/2))^2