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sinh(2*z)=-4*i la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
sinh(2*z) = -4*I
sinh⁡(2z)=−4i\sinh{\left(2 z \right)} = - 4 i
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Gráfica
Suma y producto de raíces [src] 
suma
            /   ____________\               /   ____________\               /   ____________\               /   ____________\
  pi*I      |  /       ____ |   3*pi*I      |  /       ____ |     pi*I      |  /       ____ |   3*pi*I      |  /       ____ |
- ---- + log\\/  4 - \/ 15  / + ------ + log\\/  4 - \/ 15  / + - ---- + log\\/  4 + \/ 15  / + ------ + log\\/  4 + \/ 15  /
   4                              4                                4                              4
((log⁡(15+4)−iπ4)+((log⁡(4−15)−iπ4)+(log⁡(4−15)+3iπ4)))+(log⁡(15+4)+3iπ4)\left(\left(\log{\left(\sqrt{\sqrt{15} + 4} \right)} - \frac{i \pi}{4}\right) + \left(\left(\log{\left(\sqrt{4 - \sqrt{15}} \right)} - \frac{i \pi}{4}\right) + \left(\log{\left(\sqrt{4 - \sqrt{15}} \right)} + \frac{3 i \pi}{4}\right)\right)\right) + \left(\log{\left(\sqrt{\sqrt{15} + 4} \right)} + \frac{3 i \pi}{4}\right) 
=
     /   ____________\        /   ____________\       
     |  /       ____ |        |  /       ____ |       
2*log\\/  4 + \/ 15  / + 2*log\\/  4 - \/ 15  / + pi*I
2log⁡(4−15)+2log⁡(15+4)+iπ2 \log{\left(\sqrt{4 - \sqrt{15}} \right)} + 2 \log{\left(\sqrt{\sqrt{15} + 4} \right)} + i \pi 
producto
/            /   ____________\\ /            /   ____________\\ /            /   ____________\\ /            /   ____________\\
|  pi*I      |  /       ____ || |3*pi*I      |  /       ____ || |  pi*I      |  /       ____ || |3*pi*I      |  /       ____ ||
|- ---- + log\\/  4 - \/ 15  /|*|------ + log\\/  4 - \/ 15  /|*|- ---- + log\\/  4 + \/ 15  /|*|------ + log\\/  4 + \/ 15  /|
\   4                         / \  4                          / \   4                         / \  4                          /
(log⁡(4−15)−iπ4)(log⁡(4−15)+3iπ4)(log⁡(15+4)−iπ4)(log⁡(15+4)+3iπ4)\left(\log{\left(\sqrt{4 - \sqrt{15}} \right)} - \frac{i \pi}{4}\right) \left(\log{\left(\sqrt{4 - \sqrt{15}} \right)} + \frac{3 i \pi}{4}\right) \left(\log{\left(\sqrt{\sqrt{15} + 4} \right)} - \frac{i \pi}{4}\right) \left(\log{\left(\sqrt{\sqrt{15} + 4} \right)} + \frac{3 i \pi}{4}\right) 
=
/     /      ____\       \ /     /      ____\         \ /     /      ____\       \ /     /      ____\         \
\2*log\4 + \/ 15 / - pi*I/*\2*log\4 + \/ 15 / + 3*pi*I/*\2*log\4 - \/ 15 / - pi*I/*\2*log\4 - \/ 15 / + 3*pi*I/
---------------------------------------------------------------------------------------------------------------
                                                      256
(2log⁡(4−15)−iπ)(2log⁡(4−15)+3iπ)(2log⁡(15+4)−iπ)(2log⁡(15+4)+3iπ)256\frac{\left(2 \log{\left(4 - \sqrt{15} \right)} - i \pi\right) \left(2 \log{\left(4 - \sqrt{15} \right)} + 3 i \pi\right) \left(2 \log{\left(\sqrt{15} + 4 \right)} - i \pi\right) \left(2 \log{\left(\sqrt{15} + 4 \right)} + 3 i \pi\right)}{256} 
(2*log(4 + sqrt(15)) - pi*i)*(2*log(4 + sqrt(15)) + 3*pi*i)*(2*log(4 - sqrt(15)) - pi*i)*(2*log(4 - sqrt(15)) + 3*pi*i)/256
Respuesta rápida [src] 
                 /   ____________\
       pi*I      |  /       ____ |
z1 = - ---- + log\\/  4 - \/ 15  /
        4
z1=log⁡(4−15)−iπ4z_{1} = \log{\left(\sqrt{4 - \sqrt{15}} \right)} - \frac{i \pi}{4} 
                 /   ____________\
     3*pi*I      |  /       ____ |
z2 = ------ + log\\/  4 - \/ 15  /
       4
z2=log⁡(4−15)+3iπ4z_{2} = \log{\left(\sqrt{4 - \sqrt{15}} \right)} + \frac{3 i \pi}{4} 
                 /   ____________\
       pi*I      |  /       ____ |
z3 = - ---- + log\\/  4 + \/ 15  /
        4
z3=log⁡(15+4)−iπ4z_{3} = \log{\left(\sqrt{\sqrt{15} + 4} \right)} - \frac{i \pi}{4} 
                 /   ____________\
     3*pi*I      |  /       ____ |
z4 = ------ + log\\/  4 + \/ 15  /
       4
z4=log⁡(15+4)+3iπ4z_{4} = \log{\left(\sqrt{\sqrt{15} + 4} \right)} + \frac{3 i \pi}{4} 
z4 = log(sqrt(sqrt(15) + 4)) + 3*i*pi/4
Respuesta numérica [src] 
z1 = -1.03171853444778 - 0.785398163397448*i
z2 = -1.03171853444778 + 2.35619449019234*i
z3 = 1.03171853444778 - 0.785398163397448*i
z4 = 1.03171853444778 + 2.35619449019234*i
z4 = 1.03171853444778 + 2.35619449019234*i
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