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ln(sin(2xy^2)) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   /   /     2\\    
log\sin\2*x*y // = 0
log⁡(sin⁡(2xy2))=0\log{\left(\sin{\left(2 x y^{2} \right)} \right)} = 0
Simplificar
Gráfica
Respuesta rápida [src] 
        /        2                    2         \                       
        |      re (y)               im (y)      |                       
     pi*|------------------ - ------------------|                       
        |                 2                    2|                       
        |/  2        2   \    /  2        2   \ |                       
        \\im (y) + re (y)/    \im (y) + re (y)/ /     pi*I*im(y)*re(y)  
x1 = -------------------------------------------- - --------------------
                          4                                            2
                                                      /  2        2   \ 
                                                    2*\im (y) + re (y)/
x1=π((re⁡(y))2((re⁡(y))2+(im⁡(y))2)2−(im⁡(y))2((re⁡(y))2+(im⁡(y))2)2)4−iπre⁡(y)im⁡(y)2((re⁡(y))2+(im⁡(y))2)2x_{1} = \frac{\pi \left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right)}{4} - \frac{i \pi \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} 
x1 = pi*(re(y)^2/(re(y)^2 + im(y)^2)^2 - im(y)^2/(re(y)^2 + im(y)^2)^2)/4 - i*pi*re(y)*im(y)/(2*(re(y)^2 + im(y)^2)^2)
Suma y producto de raíces [src] 
suma
   /        2                    2         \                       
   |      re (y)               im (y)      |                       
pi*|------------------ - ------------------|                       
   |                 2                    2|                       
   |/  2        2   \    /  2        2   \ |                       
   \\im (y) + re (y)/    \im (y) + re (y)/ /     pi*I*im(y)*re(y)  
-------------------------------------------- - --------------------
                     4                                            2
                                                 /  2        2   \ 
                                               2*\im (y) + re (y)/
π((re⁡(y))2((re⁡(y))2+(im⁡(y))2)2−(im⁡(y))2((re⁡(y))2+(im⁡(y))2)2)4−iπre⁡(y)im⁡(y)2((re⁡(y))2+(im⁡(y))2)2\frac{\pi \left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right)}{4} - \frac{i \pi \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} 
=
   /        2                    2         \                       
   |      re (y)               im (y)      |                       
pi*|------------------ - ------------------|                       
   |                 2                    2|                       
   |/  2        2   \    /  2        2   \ |                       
   \\im (y) + re (y)/    \im (y) + re (y)/ /     pi*I*im(y)*re(y)  
-------------------------------------------- - --------------------
                     4                                            2
                                                 /  2        2   \ 
                                               2*\im (y) + re (y)/
π((re⁡(y))2((re⁡(y))2+(im⁡(y))2)2−(im⁡(y))2((re⁡(y))2+(im⁡(y))2)2)4−iπre⁡(y)im⁡(y)2((re⁡(y))2+(im⁡(y))2)2\frac{\pi \left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right)}{4} - \frac{i \pi \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} 
producto
   /        2                    2         \                       
   |      re (y)               im (y)      |                       
pi*|------------------ - ------------------|                       
   |                 2                    2|                       
   |/  2        2   \    /  2        2   \ |                       
   \\im (y) + re (y)/    \im (y) + re (y)/ /     pi*I*im(y)*re(y)  
-------------------------------------------- - --------------------
                     4                                            2
                                                 /  2        2   \ 
                                               2*\im (y) + re (y)/
π((re⁡(y))2((re⁡(y))2+(im⁡(y))2)2−(im⁡(y))2((re⁡(y))2+(im⁡(y))2)2)4−iπre⁡(y)im⁡(y)2((re⁡(y))2+(im⁡(y))2)2\frac{\pi \left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right)}{4} - \frac{i \pi \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} 
=
   /  2        2                     \
pi*\re (y) - im (y) - 2*I*im(y)*re(y)/
--------------------------------------
                            2         
           /  2        2   \          
         4*\im (y) + re (y)/
π((re⁡(y))2−2ire⁡(y)im⁡(y)−(im⁡(y))2)4((re⁡(y))2+(im⁡(y))2)2\frac{\pi \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{4 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} 
pi*(re(y)^2 - im(y)^2 - 2*i*im(y)*re(y))/(4*(im(y)^2 + re(y)^2)^2)
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