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arctg(x^2+y^2-2x-3)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
    / 2    2          \    
atan\x  + y  - 2*x - 3/ = 0
atan⁡((−2x+(x2+y2))−3)=0\operatorname{atan}{\left(\left(- 2 x + \left(x^{2} + y^{2}\right)\right) - 3 \right)} = 0
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Gráfica
Respuesta rápida [src] 
             __________________________________________                                                         __________________________________________                                                
            /                      2                       /     /                      2        2   \\        /                      2                       /     /                      2        2   \\
         4 /  /      2        2   \        2      2        |atan2\-2*im(y)*re(y), 4 + im (y) - re (y)/|     4 /  /      2        2   \        2      2        |atan2\-2*im(y)*re(y), 4 + im (y) - re (y)/|
x1 = 1 - \/   \4 + im (y) - re (y)/  + 4*im (y)*re (y) *cos|------------------------------------------| - I*\/   \4 + im (y) - re (y)/  + 4*im (y)*re (y) *sin|------------------------------------------|
                                                           \                    2                     /                                                       \                    2                     /
x1=−i(−(re⁡(y))2+(im⁡(y))2+4)2+4(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2+4)2)−(−(re⁡(y))2+(im⁡(y))2+4)2+4(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2+4)2)+1x_{1} = - i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4\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} + 4 \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4\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} + 4 \right)}}{2} \right)} + 1 
             __________________________________________                                                         __________________________________________                                                
            /                      2                       /     /                      2        2   \\        /                      2                       /     /                      2        2   \\
         4 /  /      2        2   \        2      2        |atan2\-2*im(y)*re(y), 4 + im (y) - re (y)/|     4 /  /      2        2   \        2      2        |atan2\-2*im(y)*re(y), 4 + im (y) - re (y)/|
x2 = 1 + \/   \4 + im (y) - re (y)/  + 4*im (y)*re (y) *cos|------------------------------------------| + I*\/   \4 + im (y) - re (y)/  + 4*im (y)*re (y) *sin|------------------------------------------|
                                                           \                    2                     /                                                       \                    2                     /
x2=i(−(re⁡(y))2+(im⁡(y))2+4)2+4(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2+4)2)+(−(re⁡(y))2+(im⁡(y))2+4)2+4(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2+4)2)+1x_{2} = i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4\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} + 4 \right)}}{2} \right)} + \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4\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} + 4 \right)}}{2} \right)} + 1 
x2 = i*((-re(y)^2 + im(y)^2 + 4)^2 + 4*re(y)^2*im(y)^2)^(1/4)*sin(atan2(-2*re(y)*im(y, -re(y)^2 + im(y)^2 + 4)/2) + ((-re(y)^2 + im(y)^2 + 4)^2 + 4*re(y)^2*im(y)^2)^(1/4)*cos(atan2(-2*re(y)*im(y), -re(y)^2 + im(y)^2 + 4)/2) + 1)
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), 4 + im (y) - re (y)/|     4 /  /      2        2   \        2      2        |atan2\-2*im(y)*re(y), 4 + im (y) - re (y)/|       4 /  /      2        2   \        2      2        |atan2\-2*im(y)*re(y), 4 + im (y) - re (y)/|     4 /  /      2        2   \        2      2        |atan2\-2*im(y)*re(y), 4 + im (y) - re (y)/|
1 - \/   \4 + im (y) - re (y)/  + 4*im (y)*re (y) *cos|------------------------------------------| - I*\/   \4 + im (y) - re (y)/  + 4*im (y)*re (y) *sin|------------------------------------------| + 1 + \/   \4 + im (y) - re (y)/  + 4*im (y)*re (y) *cos|------------------------------------------| + I*\/   \4 + im (y) - re (y)/  + 4*im (y)*re (y) *sin|------------------------------------------|
                                                      \                    2                     /                                                       \                    2                     /                                                         \                    2                     /                                                       \                    2                     /
(−i(−(re⁡(y))2+(im⁡(y))2+4)2+4(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2+4)2)−(−(re⁡(y))2+(im⁡(y))2+4)2+4(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2+4)2)+1)+(i(−(re⁡(y))2+(im⁡(y))2+4)2+4(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2+4)2)+(−(re⁡(y))2+(im⁡(y))2+4)2+4(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2+4)2)+1)\left(- i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4\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} + 4 \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4\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} + 4 \right)}}{2} \right)} + 1\right) + \left(i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4\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} + 4 \right)}}{2} \right)} + \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4\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} + 4 \right)}}{2} \right)} + 1\right) 
=
2
22 
producto
/        __________________________________________                                                         __________________________________________                                                \ /        __________________________________________                                                         __________________________________________                                                \
|       /                      2                       /     /                      2        2   \\        /                      2                       /     /                      2        2   \\| |       /                      2                       /     /                      2        2   \\        /                      2                       /     /                      2        2   \\|
|    4 /  /      2        2   \        2      2        |atan2\-2*im(y)*re(y), 4 + im (y) - re (y)/|     4 /  /      2        2   \        2      2        |atan2\-2*im(y)*re(y), 4 + im (y) - re (y)/|| |    4 /  /      2        2   \        2      2        |atan2\-2*im(y)*re(y), 4 + im (y) - re (y)/|     4 /  /      2        2   \        2      2        |atan2\-2*im(y)*re(y), 4 + im (y) - re (y)/||
|1 - \/   \4 + im (y) - re (y)/  + 4*im (y)*re (y) *cos|------------------------------------------| - I*\/   \4 + im (y) - re (y)/  + 4*im (y)*re (y) *sin|------------------------------------------||*|1 + \/   \4 + im (y) - re (y)/  + 4*im (y)*re (y) *cos|------------------------------------------| + I*\/   \4 + im (y) - re (y)/  + 4*im (y)*re (y) *sin|------------------------------------------||
\                                                      \                    2                     /                                                       \                    2                     // \                                                      \                    2                     /                                                       \                    2                     //
(−i(−(re⁡(y))2+(im⁡(y))2+4)2+4(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2+4)2)−(−(re⁡(y))2+(im⁡(y))2+4)2+4(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2+4)2)+1)(i(−(re⁡(y))2+(im⁡(y))2+4)2+4(re⁡(y))2(im⁡(y))24sin⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2+4)2)+(−(re⁡(y))2+(im⁡(y))2+4)2+4(re⁡(y))2(im⁡(y))24cos⁡(atan2⁡(−2re⁡(y)im⁡(y),−(re⁡(y))2+(im⁡(y))2+4)2)+1)\left(- i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4\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} + 4 \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4\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} + 4 \right)}}{2} \right)} + 1\right) \left(i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4\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} + 4 \right)}}{2} \right)} + \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4\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} + 4 \right)}}{2} \right)} + 1\right) 
=
       2        2                     
-3 + re (y) - im (y) + 2*I*im(y)*re(y)
(re⁡(y))2+2ire⁡(y)im⁡(y)−(im⁡(y))2−3\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} - 3 
-3 + re(y)^2 - im(y)^2 + 2*i*im(y)*re(y)
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