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sqrt(x^2+y^2)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   _________    
  /  2    2     
\/  x  + y   = 0
x2+y2=0\sqrt{x^{2} + y^{2}} = 0
Simplificar
Solución detallada
x2+y2=0\sqrt{x^{2} + y^{2}} = 0
cambiamos
x2+y2=0x^{2} + y^{2} = 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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
donde D = b^2 - 4*a*c es el discriminante.
Como
a=1a = 1
b=0b = 0
c=y2c = y^{2}
, entonces
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (y^2) = -4*y^2

La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

o
x1=−y2x_{1} = \sqrt{- y^{2}}
x2=−−y2x_{2} = - \sqrt{- y^{2}}
Gráfica
Respuesta rápida [src] 
           ______________________________________                                                     ______________________________________                                            
          /                  2                       /     /                  2        2   \\        /                  2                       /     /                  2        2   \\
       4 /  /  2        2   \        2      2        |atan2\-2*im(y)*re(y), im (y) - re (y)/|     4 /  /  2        2   \        2      2        |atan2\-2*im(y)*re(y), im (y) - re (y)/|
x1 = - \/   \im (y) - re (y)/  + 4*im (y)*re (y) *cos|--------------------------------------| - I*\/   \im (y) - re (y)/  + 4*im (y)*re (y) *sin|--------------------------------------|
                                                     \                  2                   /                                                   \                  2                   /
x1=−i(−(re⁡(y))2+(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)2)−(−(re⁡(y))2+(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)2)x_{1} = - i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} 
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        /                  2                       /     /                  2        2   \\        /                  2                       /     /                  2        2   \\
     4 /  /  2        2   \        2      2        |atan2\-2*im(y)*re(y), im (y) - re (y)/|     4 /  /  2        2   \        2      2        |atan2\-2*im(y)*re(y), im (y) - re (y)/|
x2 = \/   \im (y) - re (y)/  + 4*im (y)*re (y) *cos|--------------------------------------| + I*\/   \im (y) - re (y)/  + 4*im (y)*re (y) *sin|--------------------------------------|
                                                   \                  2                   /                                                   \                  2                   /
x2=i(−(re⁡(y))2+(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)2)+(−(re⁡(y))2+(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)2)x_{2} = i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} 
x2 = i*((-re(y)^2 + im(y)^2)^2 + 4*re(y)^2*im(y)^2)^(1/4)*sin(atan2(-2*re(y)*im(y, -re(y)^2 + im(y)^2)/2) + ((-re(y)^2 + im(y)^2)^2 + 4*re(y)^2*im(y)^2)^(1/4)*cos(atan2(-2*re(y)*im(y), -re(y)^2 + im(y)^2)/2))
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(y)*re(y), im (y) - re (y)/|     4 /  /  2        2   \        2      2        |atan2\-2*im(y)*re(y), im (y) - re (y)/|   4 /  /  2        2   \        2      2        |atan2\-2*im(y)*re(y), im (y) - re (y)/|     4 /  /  2        2   \        2      2        |atan2\-2*im(y)*re(y), im (y) - re (y)/|
- \/   \im (y) - re (y)/  + 4*im (y)*re (y) *cos|--------------------------------------| - I*\/   \im (y) - re (y)/  + 4*im (y)*re (y) *sin|--------------------------------------| + \/   \im (y) - re (y)/  + 4*im (y)*re (y) *cos|--------------------------------------| + I*\/   \im (y) - re (y)/  + 4*im (y)*re (y) *sin|--------------------------------------|
                                                \                  2                   /                                                   \                  2                   /                                                 \                  2                   /                                                   \                  2                   /
(−i(−(re⁡(y))2+(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)2)−(−(re⁡(y))2+(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)2))+(i(−(re⁡(y))2+(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)2)+(−(re⁡(y))2+(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)2))\left(- i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \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(y)*re(y), im (y) - re (y)/|     4 /  /  2        2   \        2      2        |atan2\-2*im(y)*re(y), im (y) - re (y)/|| |4 /  /  2        2   \        2      2        |atan2\-2*im(y)*re(y), im (y) - re (y)/|     4 /  /  2        2   \        2      2        |atan2\-2*im(y)*re(y), im (y) - re (y)/||
|- \/   \im (y) - re (y)/  + 4*im (y)*re (y) *cos|--------------------------------------| - I*\/   \im (y) - re (y)/  + 4*im (y)*re (y) *sin|--------------------------------------||*|\/   \im (y) - re (y)/  + 4*im (y)*re (y) *cos|--------------------------------------| + I*\/   \im (y) - re (y)/  + 4*im (y)*re (y) *sin|--------------------------------------||
\                                                \                  2                   /                                                   \                  2                   // \                                              \                  2                   /                                                   \                  2                   //
(−i(−(re⁡(y))2+(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)2)−(−(re⁡(y))2+(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)2))(i(−(re⁡(y))2+(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)2)+(−(re⁡(y))2+(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)2))\left(- i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right) 
=
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    /                  2                            /                  2        2   \
   /  /  2        2   \        2      2      I*atan2\-2*im(y)*re(y), im (y) - re (y)/
-\/   \re (y) - im (y)/  + 4*im (y)*re (y) *e
−((re⁡(y))2−(im⁡(y))2)2+4(re⁡(y))2(im⁡(y))2eiatan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2)- \sqrt{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}} 
-sqrt((re(y)^2 - im(y)^2)^2 + 4*im(y)^2*re(y)^2)*exp(i*atan2(-2*im(y)*re(y), im(y)^2 - re(y)^2))
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