Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x + b y + c = 0$$
Коэффициент при x равен
$$a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$b y + c - x = 0$$
su solución
$$x = b y + c$$
Con
$$a = 0$$
la ecuación será
$$b y + c = 0$$
su solución
Suma y producto de raíces
[src]
/(re(c) + re(b*y))*im(a) (im(c) + im(b*y))*re(a)\ (im(c) + im(b*y))*im(a) (re(c) + re(b*y))*re(a)
I*|----------------------- - -----------------------| - ----------------------- - -----------------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$i \left(\frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
/(re(c) + re(b*y))*im(a) (im(c) + im(b*y))*re(a)\ (im(c) + im(b*y))*im(a) (re(c) + re(b*y))*re(a)
I*|----------------------- - -----------------------| - ----------------------- - -----------------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$i \left(\frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
/(re(c) + re(b*y))*im(a) (im(c) + im(b*y))*re(a)\ (im(c) + im(b*y))*im(a) (re(c) + re(b*y))*re(a)
I*|----------------------- - -----------------------| - ----------------------- - -----------------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$i \left(\frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
I*((re(c) + re(b*y))*im(a) - (im(c) + im(b*y))*re(a)) - (im(c) + im(b*y))*im(a) - (re(c) + re(b*y))*re(a)
---------------------------------------------------------------------------------------------------------
2 2
im (a) + re (a)
$$\frac{i \left(\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)} - \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}\right) - \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
(i*((re(c) + re(b*y))*im(a) - (im(c) + im(b*y))*re(a)) - (im(c) + im(b*y))*im(a) - (re(c) + re(b*y))*re(a))/(im(a)^2 + re(a)^2)
/(re(c) + re(b*y))*im(a) (im(c) + im(b*y))*re(a)\ (im(c) + im(b*y))*im(a) (re(c) + re(b*y))*re(a)
x1 = I*|----------------------- - -----------------------| - ----------------------- - -----------------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$x_{1} = i \left(\frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x1 = i*((re(c) + re(b*y))*im(a)/(re(a)^2 + im(a)^2) - (im(c) + im(b*y))*re(a)/(re(a)^2 + im(a)^2)) - (re(c) + re(b*y))*re(a)/(re(a)^2 + im(a)^2) - (im(c) + im(b*y))*im(a)/(re(a)^2 + im(a)^2)