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ln(sqrt(x^2+y^2)) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   /   _________\    
   |  /  2    2 |    
log\\/  x  + y  / = 0
log⁡(x2+y2)=0\log{\left(\sqrt{x^{2} + y^{2}} \right)} = 0
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
      __________________________________________                                                         __________________________________________                                                       __________________________________________                                                         __________________________________________                                                
     /                      2                       /     /                      2        2   \\        /                      2                       /     /                      2        2   \\      /                      2                       /     /                      2        2   \\        /                      2                       /     /                      2        2   \\
  4 /  /      2        2   \        2      2        |atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/|     4 /  /      2        2   \        2      2        |atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/|   4 /  /      2        2   \        2      2        |atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/|     4 /  /      2        2   \        2      2        |atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/|
- \/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *cos|------------------------------------------| - I*\/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *sin|------------------------------------------| + \/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *cos|------------------------------------------| + I*\/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *sin|------------------------------------------|
                                                    \                    2                     /                                                       \                    2                     /                                                     \                    2                     /                                                       \                    2                     /
(−i(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))24sin⁡(atan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)2)−(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))24cos⁡(atan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)2))+(i(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))24sin⁡(atan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)2)+(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))24cos⁡(atan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)2))\left(- i \sqrt[4]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}}{2} \right)}\right) 
=
0
00 
producto
/      __________________________________________                                                         __________________________________________                                                \ /    __________________________________________                                                         __________________________________________                                                \
|     /                      2                       /     /                      2        2   \\        /                      2                       /     /                      2        2   \\| |   /                      2                       /     /                      2        2   \\        /                      2                       /     /                      2        2   \\|
|  4 /  /      2        2   \        2      2        |atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/|     4 /  /      2        2   \        2      2        |atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/|| |4 /  /      2        2   \        2      2        |atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/|     4 /  /      2        2   \        2      2        |atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/||
|- \/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *cos|------------------------------------------| - I*\/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *sin|------------------------------------------||*|\/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *cos|------------------------------------------| + I*\/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *sin|------------------------------------------||
\                                                    \                    2                     /                                                       \                    2                     // \                                                  \                    2                     /                                                       \                    2                     //
(−i(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))24sin⁡(atan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)2)−(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))24cos⁡(atan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)2))(i(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))24sin⁡(atan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)2)+(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))24cos⁡(atan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)2))\left(- i \sqrt[4]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}}{2} \right)}\right) 
=
     __________________________________________                                              
    /                      2                            /                      2        2   \
   /  /      2        2   \        2      2      I*atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/
-\/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *e
−(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))2eiatan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)- \sqrt{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}} 
-sqrt((1 + im(x)^2 - re(x)^2)^2 + 4*im(x)^2*re(x)^2)*exp(i*atan2(-2*im(x)*re(x), 1 + im(x)^2 - re(x)^2))
Respuesta rápida [src] 
           __________________________________________                                                         __________________________________________                                                
          /                      2                       /     /                      2        2   \\        /                      2                       /     /                      2        2   \\
       4 /  /      2        2   \        2      2        |atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/|     4 /  /      2        2   \        2      2        |atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/|
y1 = - \/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *cos|------------------------------------------| - I*\/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *sin|------------------------------------------|
                                                         \                    2                     /                                                       \                    2                     /
y1=−i(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))24sin⁡(atan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)2)−(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))24cos⁡(atan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)2)y_{1} = - i \sqrt[4]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}}{2} \right)} 
         __________________________________________                                                         __________________________________________                                                
        /                      2                       /     /                      2        2   \\        /                      2                       /     /                      2        2   \\
     4 /  /      2        2   \        2      2        |atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/|     4 /  /      2        2   \        2      2        |atan2\-2*im(x)*re(x), 1 + im (x) - re (x)/|
y2 = \/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *cos|------------------------------------------| + I*\/   \1 + im (x) - re (x)/  + 4*im (x)*re (x) *sin|------------------------------------------|
                                                       \                    2                     /                                                       \                    2                     /
y2=i(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))24sin⁡(atan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)2)+(−(re⁡(x))2+(im⁡(x))2+1)2+4(re⁡(x))2(im⁡(x))24cos⁡(atan2⁡(−2re⁡(x)im⁡(x),−(re⁡(x))2+(im⁡(x))2+1)2)y_{2} = i \sqrt[4]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1 \right)}}{2} \right)} 
y2 = i*((-re(x)^2 + im(x)^2 + 1)^2 + 4*re(x)^2*im(x)^2)^(1/4)*sin(atan2(-2*re(x)*im(x, -re(x)^2 + im(x)^2 + 1)/2) + ((-re(x)^2 + im(x)^2 + 1)^2 + 4*re(x)^2*im(x)^2)^(1/4)*cos(atan2(-2*re(x)*im(x), -re(x)^2 + im(x)^2 + 1)/2))
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