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arctg(c)+arctg(x)=-arctg(y) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
atan(c) + atan(x) = -atan(y)
atan⁡(c)+atan⁡(x)=−atan⁡(y)\operatorname{atan}{\left(c \right)} + \operatorname{atan}{\left(x \right)} = - \operatorname{atan}{\left(y \right)}
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
  /(-1 + re(c*y))*(im(c) + im(y))    (re(c) + re(y))*im(c*y)  \   (-1 + re(c*y))*(re(c) + re(y))    (im(c) + im(y))*im(c*y)  
I*|------------------------------ - --------------------------| + ------------------------------ + --------------------------
  |                2     2                        2     2     |                   2     2                        2     2     
  \  (-1 + re(c*y))  + im (c*y)     (-1 + re(c*y))  + im (c*y)/     (-1 + re(c*y))  + im (c*y)     (-1 + re(c*y))  + im (c*y)
i(−(re⁡(c)+re⁡(y))im⁡(cy)(re⁡(cy)−1)2+(im⁡(cy))2+(re⁡(cy)−1)(im⁡(c)+im⁡(y))(re⁡(cy)−1)2+(im⁡(cy))2)+(re⁡(c)+re⁡(y))(re⁡(cy)−1)(re⁡(cy)−1)2+(im⁡(cy))2+(im⁡(c)+im⁡(y))im⁡(cy)(re⁡(cy)−1)2+(im⁡(cy))2i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(c y\right)} - 1\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right)}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c y\right)} - 1\right)}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} 
=
  /(-1 + re(c*y))*(im(c) + im(y))    (re(c) + re(y))*im(c*y)  \   (-1 + re(c*y))*(re(c) + re(y))    (im(c) + im(y))*im(c*y)  
I*|------------------------------ - --------------------------| + ------------------------------ + --------------------------
  |                2     2                        2     2     |                   2     2                        2     2     
  \  (-1 + re(c*y))  + im (c*y)     (-1 + re(c*y))  + im (c*y)/     (-1 + re(c*y))  + im (c*y)     (-1 + re(c*y))  + im (c*y)
i(−(re⁡(c)+re⁡(y))im⁡(cy)(re⁡(cy)−1)2+(im⁡(cy))2+(re⁡(cy)−1)(im⁡(c)+im⁡(y))(re⁡(cy)−1)2+(im⁡(cy))2)+(re⁡(c)+re⁡(y))(re⁡(cy)−1)(re⁡(cy)−1)2+(im⁡(cy))2+(im⁡(c)+im⁡(y))im⁡(cy)(re⁡(cy)−1)2+(im⁡(cy))2i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(c y\right)} - 1\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right)}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c y\right)} - 1\right)}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} 
producto
  /(-1 + re(c*y))*(im(c) + im(y))    (re(c) + re(y))*im(c*y)  \   (-1 + re(c*y))*(re(c) + re(y))    (im(c) + im(y))*im(c*y)  
I*|------------------------------ - --------------------------| + ------------------------------ + --------------------------
  |                2     2                        2     2     |                   2     2                        2     2     
  \  (-1 + re(c*y))  + im (c*y)     (-1 + re(c*y))  + im (c*y)/     (-1 + re(c*y))  + im (c*y)     (-1 + re(c*y))  + im (c*y)
i(−(re⁡(c)+re⁡(y))im⁡(cy)(re⁡(cy)−1)2+(im⁡(cy))2+(re⁡(cy)−1)(im⁡(c)+im⁡(y))(re⁡(cy)−1)2+(im⁡(cy))2)+(re⁡(c)+re⁡(y))(re⁡(cy)−1)(re⁡(cy)−1)2+(im⁡(cy))2+(im⁡(c)+im⁡(y))im⁡(cy)(re⁡(cy)−1)2+(im⁡(cy))2i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(c y\right)} - 1\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right)}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c y\right)} - 1\right)}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} 
=
I*((-1 + re(c*y))*(im(c) + im(y)) - (re(c) + re(y))*im(c*y)) + (-1 + re(c*y))*(re(c) + re(y)) + (im(c) + im(y))*im(c*y)
-----------------------------------------------------------------------------------------------------------------------
                                                             2     2                                                   
                                               (-1 + re(c*y))  + im (c*y)
i(−(re⁡(c)+re⁡(y))im⁡(cy)+(re⁡(cy)−1)(im⁡(c)+im⁡(y)))+(re⁡(c)+re⁡(y))(re⁡(cy)−1)+(im⁡(c)+im⁡(y))im⁡(cy)(re⁡(cy)−1)2+(im⁡(cy))2\frac{i \left(- \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)} + \left(\operatorname{re}{\left(c y\right)} - 1\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right)\right) + \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c y\right)} - 1\right) + \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(c y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c y\right)}\right)^{2}} 
(i*((-1 + re(c*y))*(im(c) + im(y)) - (re(c) + re(y))*im(c*y)) + (-1 + re(c*y))*(re(c) + re(y)) + (im(c) + im(y))*im(c*y))/((-1 + re(c*y))^2 + im(c*y)^2)
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