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- La ecuación:
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Ecuación x^4+2*x^2-8=0
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Ecuación x*(x^2+8*x+16)=5*(x+4)
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Ecuación -25-x=-17
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Ecuación x^2+3x=4
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- -17*x+1*y=-11
-
Expresiones idénticas
- tgπ(4x− cinco) seis = tres –√ tres
- tgπ(4x−5)6 es igual a 3–√3
- tgπ(4x− cinco) seis es igual a tres –√ tres
- tgπ4x−56=3–√3
tgπ(4x−5)6=3–√3 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___ tan(p)*I*(4*x - 5)*6 = 3 - \/ 3
$$6 i \tan{\left(p \right)} \left(4 x - 5\right) = 3 - \sqrt{3}$$
Solución detallada
Tenemos la ecuación
$$6 i \tan{\left(p \right)} \left(4 x - 5\right) = 3 - \sqrt{3}$$
cambiamos
$$6 i \left(4 x - 5\right) \tan{\left(p \right)} - 4 + \sqrt{3} = 0$$
$$6 i \tan{\left(p \right)} \left(4 x - 5\right) - 4 + \sqrt{3} = 0$$
Sustituimos
$$w = \tan{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$6 i w \left(4 x - 5\right) + \sqrt{3} = 4$$
Dividamos ambos miembros de la ecuación en (sqrt(3) + 6*i*w*(-5 + 4*x))/w
Obtenemos la respuesta: w = i*(-4 + sqrt(3))/(6*(-5 + 4*x))
hacemos cambio inverso
$$\tan{\left(p \right)} = w$$
sustituimos w:
$$6 i \tan{\left(p \right)} \left(4 x - 5\right) = 3 - \sqrt{3}$$
cambiamos
$$6 i \left(4 x - 5\right) \tan{\left(p \right)} - 4 + \sqrt{3} = 0$$
$$6 i \tan{\left(p \right)} \left(4 x - 5\right) - 4 + \sqrt{3} = 0$$
Sustituimos
$$w = \tan{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-4 + sqrt3 + 6*i*w4*x+5 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-4 + sqrt(3) + 6*i*w*(-5 + 4*x) = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$6 i w \left(4 x - 5\right) + \sqrt{3} = 4$$
Dividamos ambos miembros de la ecuación en (sqrt(3) + 6*i*w*(-5 + 4*x))/w
w = 4 / ((sqrt(3) + 6*i*w*(-5 + 4*x))/w)
Obtenemos la respuesta: w = i*(-4 + sqrt(3))/(6*(-5 + 4*x))
hacemos cambio inverso
$$\tan{\left(p \right)} = w$$
sustituimos w:
Gráfica
Respuesta rápida
[src]
/ / ___ 30*sinh(2*im(p)) \ \ / ___ 30*sinh(2*im(p)) \
| |-3 + \/ 3 + ----------------------------|*sin(2*re(p)) | 2 |-3 + \/ 3 + ----------------------------|*sinh(2*im(p))
| 5*sin(2*re(p))*sinh(2*im(p)) \ cos(2*re(p)) + cosh(2*im(p))/ | 5*sin (2*re(p)) \ cos(2*re(p)) + cosh(2*im(p))/
x1 = I*|- ----------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
| | sin (2*re(p)) sinh (2*im(p)) | 2 | sin (2*re(p)) sinh (2*im(p)) | | | sin (2*re(p)) sinh (2*im(p)) | 2 | sin (2*re(p)) sinh (2*im(p)) |
| 4*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) 24*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p)))| 4*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) 24*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p)))
| | 2 2| | 2 2| | | 2 2| | 2 2|
\ \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) /
$$x_{1} = i \left(\frac{\left(-3 + \sqrt{3} + \frac{30 \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}}\right) \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{24 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{5 \sin{\left(2 \operatorname{re}{\left(p\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{4 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) + \frac{\left(-3 + \sqrt{3} + \frac{30 \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}}\right) \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{24 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} + \frac{5 \sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{4 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}$$
x1 = i*((-3 + sqrt(3) + 30*sinh(2*im(p))/(cos(2*re(p)) + cosh(2*im(p))))*sin(2*re(p))/(24*(sin(2*re(p))^2/(cos(2*re(p)) + cosh(2*im(p)))^2 + sinh(2*im(p))^2/(cos(2*re(p)) + cosh(2*im(p)))^2)*(cos(2*re(p)) + cosh(2*im(p)))) - 5*sin(2*re(p))*sinh(2*im(p))/(4*(sin(2*re(p))^2/(cos(2*re(p)) + cosh(2*im(p)))^2 + sinh(2*im(p))^2/(cos(2*re(p)) + cosh(2*im(p)))^2)*(cos(2*re(p)) + cosh(2*im(p)))^2)) + (-3 + sqrt(3) + 30*sinh(2*im(p))/(cos(2*re(p)) + cosh(2*im(p))))*sinh(2*im(p))/(24*(sin(2*re(p))^2/(cos(2*re(p)) + cosh(2*im(p)))^2 + sinh(2*im(p))^2/(cos(2*re(p)) + cosh(2*im(p)))^2)*(cos(2*re(p)) + cosh(2*im(p)))) + 5*sin(2*re(p))^2/(4*(sin(2*re(p))^2/(cos(2*re(p)) + cosh(2*im(p)))^2 + sinh(2*im(p))^2/(cos(2*re(p)) + cosh(2*im(p)))^2)*(cos(2*re(p)) + cosh(2*im(p)))^2)
Suma y producto de raíces
[src]
suma
/ / ___ 30*sinh(2*im(p)) \ \ / ___ 30*sinh(2*im(p)) \ | |-3 + \/ 3 + ----------------------------|*sin(2*re(p)) | 2 |-3 + \/ 3 + ----------------------------|*sinh(2*im(p)) | 5*sin(2*re(p))*sinh(2*im(p)) \ cos(2*re(p)) + cosh(2*im(p))/ | 5*sin (2*re(p)) \ cos(2*re(p)) + cosh(2*im(p))/ I*|- ----------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------- | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ | | sin (2*re(p)) sinh (2*im(p)) | 2 | sin (2*re(p)) sinh (2*im(p)) | | | sin (2*re(p)) sinh (2*im(p)) | 2 | sin (2*re(p)) sinh (2*im(p)) | | 4*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) 24*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p)))| 4*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) 24*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) | | 2 2| | 2 2| | | 2 2| | 2 2| \ \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) /
$$i \left(\frac{\left(-3 + \sqrt{3} + \frac{30 \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}}\right) \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{24 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{5 \sin{\left(2 \operatorname{re}{\left(p\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{4 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) + \frac{\left(-3 + \sqrt{3} + \frac{30 \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}}\right) \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{24 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} + \frac{5 \sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{4 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}$$
=
/ / ___ 30*sinh(2*im(p)) \ \ / ___ 30*sinh(2*im(p)) \ | |-3 + \/ 3 + ----------------------------|*sin(2*re(p)) | 2 |-3 + \/ 3 + ----------------------------|*sinh(2*im(p)) | 5*sin(2*re(p))*sinh(2*im(p)) \ cos(2*re(p)) + cosh(2*im(p))/ | 5*sin (2*re(p)) \ cos(2*re(p)) + cosh(2*im(p))/ I*|- ----------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------- | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ | | sin (2*re(p)) sinh (2*im(p)) | 2 | sin (2*re(p)) sinh (2*im(p)) | | | sin (2*re(p)) sinh (2*im(p)) | 2 | sin (2*re(p)) sinh (2*im(p)) | | 4*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) 24*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p)))| 4*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) 24*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) | | 2 2| | 2 2| | | 2 2| | 2 2| \ \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) /
$$i \left(\frac{\left(-3 + \sqrt{3} + \frac{30 \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}}\right) \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{24 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{5 \sin{\left(2 \operatorname{re}{\left(p\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{4 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) + \frac{\left(-3 + \sqrt{3} + \frac{30 \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}}\right) \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{24 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} + \frac{5 \sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{4 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}$$
producto
/ / ___ 30*sinh(2*im(p)) \ \ / ___ 30*sinh(2*im(p)) \ | |-3 + \/ 3 + ----------------------------|*sin(2*re(p)) | 2 |-3 + \/ 3 + ----------------------------|*sinh(2*im(p)) | 5*sin(2*re(p))*sinh(2*im(p)) \ cos(2*re(p)) + cosh(2*im(p))/ | 5*sin (2*re(p)) \ cos(2*re(p)) + cosh(2*im(p))/ I*|- ----------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------- | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ | | sin (2*re(p)) sinh (2*im(p)) | 2 | sin (2*re(p)) sinh (2*im(p)) | | | sin (2*re(p)) sinh (2*im(p)) | 2 | sin (2*re(p)) sinh (2*im(p)) | | 4*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) 24*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p)))| 4*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) 24*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) | | 2 2| | 2 2| | | 2 2| | 2 2| \ \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) /
$$i \left(\frac{\left(-3 + \sqrt{3} + \frac{30 \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}}\right) \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{24 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{5 \sin{\left(2 \operatorname{re}{\left(p\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{4 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) + \frac{\left(-3 + \sqrt{3} + \frac{30 \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}}\right) \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{24 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} + \frac{5 \sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{4 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}$$
=
/ ___ ___ \
30*sin(2*re(p)) + I*\-3*cos(2*re(p)) - 3*cosh(2*im(p)) + 30*sinh(2*im(p)) + \/ 3 *cos(2*re(p)) + \/ 3 *cosh(2*im(p))/
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24*(I*sinh(2*im(p)) + sin(2*re(p)))
$$\frac{i \left(- 3 \cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \sqrt{3} \cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + 30 \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)} - 3 \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)} + \sqrt{3} \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right) + 30 \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{24 \left(\sin{\left(2 \operatorname{re}{\left(p\right)} \right)} + i \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
(30*sin(2*re(p)) + i*(-3*cos(2*re(p)) - 3*cosh(2*im(p)) + 30*sinh(2*im(p)) + sqrt(3)*cos(2*re(p)) + sqrt(3)*cosh(2*im(p))))/(24*(i*sinh(2*im(p)) + sin(2*re(p))))