Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación x^2+5x=36
-
Ecuación 3*x=8
-
Ecuación x^2+4*x+3=0
-
Ecuación (x-87)-27=36
- Expresar {x} en función de y en la ecuación:
- -17*x+2*y=9
- 10*x-15*y=16
- -17*x+2*y=-4
- -2*x-19*y=3
-
Expresiones idénticas
- y^ dos +(dos / cinco)*y+(cuarenta y siete / doscientos cincuenta)=(uno / veinticinco)*y^ dos +(dos / cinco)*p*x+x^ dos
- y al cuadrado más (2 dividir por 5) multiplicar por y más (47 dividir por 250) es igual a (1 dividir por 25) multiplicar por y al cuadrado más (2 dividir por 5) multiplicar por p multiplicar por x más x al cuadrado
- y en el grado dos más (dos dividir por cinco) multiplicar por y más (cuarenta y siete dividir por doscientos cincuenta) es igual a (uno dividir por veinticinco) multiplicar por y en el grado dos más (dos dividir por cinco) multiplicar por p multiplicar por x más x en el grado dos
- y2+(2/5)*y+(47/250)=(1/25)*y2+(2/5)*p*x+x2
- y2+2/5*y+47/250=1/25*y2+2/5*p*x+x2
- y²+(2/5)*y+(47/250)=(1/25)*y²+(2/5)*p*x+x²
- y en el grado 2+(2/5)*y+(47/250)=(1/25)*y en el grado 2+(2/5)*p*x+x en el grado 2
- y^2+(2/5)y+(47/250)=(1/25)y^2+(2/5)px+x^2
- y2+(2/5)y+(47/250)=(1/25)y2+(2/5)px+x2
- y2+2/5y+47/250=1/25y2+2/5px+x2
- y^2+2/5y+47/250=1/25y^2+2/5px+x^2
- y^2+(2 dividir por 5)*y+(47 dividir por 250)=(1 dividir por 25)*y^2+(2 dividir por 5)*p*x+x^2
-
Expresiones semejantes
- y^2+(2/5)*y+(47/250)=(1/25)*y^2+(2/5)*p*x-x^2
- y^2-(2/5)*y+(47/250)=(1/25)*y^2+(2/5)*p*x+x^2
- y^2+(2/5)*y+(47/250)=(1/25)*y^2-(2/5)*p*x+x^2
- y^2+(2/5)*y-(47/250)=(1/25)*y^2+(2/5)*p*x+x^2
y^2+(2/5)*y+(47/250)=(1/25)*y^2+(2/5)*p*x+x^2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2
2 2*y 47 y 2*p 2
y + --- + --- = -- + ---*x + x
5 250 25 5
$$\left(y^{2} + \frac{2 y}{5}\right) + \frac{47}{250} = x^{2} + \left(\frac{2 p}{5} x + \frac{y^{2}}{25}\right)$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$\left(y^{2} + \frac{2 y}{5}\right) + \frac{47}{250} = x^{2} + \left(\frac{2 p}{5} x + \frac{y^{2}}{25}\right)$$
en
$$\left(- x^{2} + \left(- \frac{2 p}{5} x - \frac{y^{2}}{25}\right)\right) + \left(\left(y^{2} + \frac{2 y}{5}\right) + \frac{47}{250}\right) = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = -1$$
$$b = - \frac{2 p}{5}$$
$$c = \frac{24 y^{2}}{25} + \frac{2 y}{5} + \frac{47}{250}$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = - \frac{p}{5} - \frac{\sqrt{\frac{4 p^{2}}{25} + \frac{96 y^{2}}{25} + \frac{8 y}{5} + \frac{94}{125}}}{2}$$
$$x_{2} = - \frac{p}{5} + \frac{\sqrt{\frac{4 p^{2}}{25} + \frac{96 y^{2}}{25} + \frac{8 y}{5} + \frac{94}{125}}}{2}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$\left(y^{2} + \frac{2 y}{5}\right) + \frac{47}{250} = x^{2} + \left(\frac{2 p}{5} x + \frac{y^{2}}{25}\right)$$
en
$$\left(- x^{2} + \left(- \frac{2 p}{5} x - \frac{y^{2}}{25}\right)\right) + \left(\left(y^{2} + \frac{2 y}{5}\right) + \frac{47}{250}\right) = 0$$
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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = -1$$
$$b = - \frac{2 p}{5}$$
$$c = \frac{24 y^{2}}{25} + \frac{2 y}{5} + \frac{47}{250}$$
, entonces
D = b^2 - 4 * a * c =
(-2*p/5)^2 - 4 * (-1) * (47/250 + 2*y/5 + 24*y^2/25) = 94/125 + 4*p^2/25 + 8*y/5 + 96*y^2/25
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = - \frac{p}{5} - \frac{\sqrt{\frac{4 p^{2}}{25} + \frac{96 y^{2}}{25} + \frac{8 y}{5} + \frac{94}{125}}}{2}$$
$$x_{2} = - \frac{p}{5} + \frac{\sqrt{\frac{4 p^{2}}{25} + \frac{96 y^{2}}{25} + \frac{8 y}{5} + \frac{94}{125}}}{2}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(y^{2} + \frac{2 y}{5}\right) + \frac{47}{250} = x^{2} + \left(\frac{2 p}{5} x + \frac{y^{2}}{25}\right)$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{2 p x}{5} + x^{2} - \frac{24 y^{2}}{25} - \frac{2 y}{5} - \frac{47}{250} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{2 p}{5}$$
$$q = \frac{c}{a}$$
$$q = - \frac{24 y^{2}}{25} - \frac{2 y}{5} - \frac{47}{250}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{2 p}{5}$$
$$x_{1} x_{2} = - \frac{24 y^{2}}{25} - \frac{2 y}{5} - \frac{47}{250}$$
$$\left(y^{2} + \frac{2 y}{5}\right) + \frac{47}{250} = x^{2} + \left(\frac{2 p}{5} x + \frac{y^{2}}{25}\right)$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{2 p x}{5} + x^{2} - \frac{24 y^{2}}{25} - \frac{2 y}{5} - \frac{47}{250} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{2 p}{5}$$
$$q = \frac{c}{a}$$
$$q = - \frac{24 y^{2}}{25} - \frac{2 y}{5} - \frac{47}{250}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{2 p}{5}$$
$$x_{1} x_{2} = - \frac{24 y^{2}}{25} - \frac{2 y}{5} - \frac{47}{250}$$
Gráfica
Respuesta rápida
[src]
/ ________________________________________________________________________________________________________________________________ \ ________________________________________________________________________________________________________________________________
| / 2 / / 2 2 2 2 \\| / 2 / / 2 2 2 2 \\
| 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/|| 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/|
| \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------|| \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *cos|------------------------------------------------------------------------------------------------------------------------------|
re(p) | im(p) \ 2 /| \ 2 /
x1 = - ----- + I*|- ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5 \ 5 50 / 50
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{im}{\left(p\right)}}{5}\right) - \frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{re}{\left(p\right)}}{5}$$
/ ________________________________________________________________________________________________________________________________ \ ________________________________________________________________________________________________________________________________
| / 2 / / 2 2 2 2 \\| / 2 / / 2 2 2 2 \\
| 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/|| 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/|
| \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------|| \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *cos|------------------------------------------------------------------------------------------------------------------------------|
re(p) | im(p) \ 2 /| \ 2 /
x2 = - ----- + I*|- ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5 \ 5 50 / 50
$$x_{2} = i \left(\frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{im}{\left(p\right)}}{5}\right) + \frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{re}{\left(p\right)}}{5}$$
x2 = i*(((200*re(p)*im(p) + 4800*re(y)*im(y) + 1000*im(y))^2 + (100*re(p)^2 + 2400*re(y)^2 + 1000*re(y) - 100*im(p)^2 - 2400*im(y)^2 + 470)^2)^(1/4)*sin(atan2(200*re(p)*im(p) + 4800*re(y)*im(y) + 1000*im(y, 100*re(p)^2 + 2400*re(y)^2 + 1000*re(y) - 100*im(p)^2 - 2400*im(y)^2 + 470)/2)/50 - im(p)/5) + ((200*re(p)*im(p) + 4800*re(y)*im(y) + 1000*im(y))^2 + (100*re(p)^2 + 2400*re(y)^2 + 1000*re(y) - 100*im(p)^2 - 2400*im(y)^2 + 470)^2)^(1/4)*cos(atan2(200*re(p)*im(p) + 4800*re(y)*im(y) + 1000*im(y), 100*re(p)^2 + 2400*re(y)^2 + 1000*re(y) - 100*im(p)^2 - 2400*im(y)^2 + 470)/2)/50 - re(p)/5)
Suma y producto de raíces
[src]
suma
/ ________________________________________________________________________________________________________________________________ \ ________________________________________________________________________________________________________________________________ / ________________________________________________________________________________________________________________________________ \ ________________________________________________________________________________________________________________________________
| / 2 / / 2 2 2 2 \\| / 2 / / 2 2 2 2 \\ | / 2 / / 2 2 2 2 \\| / 2 / / 2 2 2 2 \\
| 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/|| 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/| | 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/|| 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/|
| \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------|| \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *cos|------------------------------------------------------------------------------------------------------------------------------| | \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------|| \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *cos|------------------------------------------------------------------------------------------------------------------------------|
re(p) | im(p) \ 2 /| \ 2 / re(p) | im(p) \ 2 /| \ 2 /
- ----- + I*|- ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + - ----- + I*|- ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5 \ 5 50 / 50 5 \ 5 50 / 50
$$\left(i \left(- \frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{im}{\left(p\right)}}{5}\right) - \frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{re}{\left(p\right)}}{5}\right) + \left(i \left(\frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{im}{\left(p\right)}}{5}\right) + \frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{re}{\left(p\right)}}{5}\right)$$
=
/ ________________________________________________________________________________________________________________________________ \ / ________________________________________________________________________________________________________________________________ \
| / 2 / / 2 2 2 2 \\| | / 2 / / 2 2 2 2 \\|
| 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/|| | 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/||
| \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------|| | \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------||
2*re(p) | im(p) \ 2 /| | im(p) \ 2 /|
- ------- + I*|- ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|- ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
5 \ 5 50 / \ 5 50 /
$$i \left(- \frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{im}{\left(p\right)}}{5}\right) + i \left(\frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{im}{\left(p\right)}}{5}\right) - \frac{2 \operatorname{re}{\left(p\right)}}{5}$$
producto
/ / ________________________________________________________________________________________________________________________________ \ ________________________________________________________________________________________________________________________________ \ / / ________________________________________________________________________________________________________________________________ \ ________________________________________________________________________________________________________________________________ \ | | / 2 / / 2 2 2 2 \\| / 2 / / 2 2 2 2 \\| | | / 2 / / 2 2 2 2 \\| / 2 / / 2 2 2 2 \\| | | 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/|| 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/|| | | 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/|| 4 / 2 / 2 2 2 2 \ |atan2\1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y), 470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/|| | | \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------|| \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *cos|------------------------------------------------------------------------------------------------------------------------------|| | | \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------|| \/ (1000*im(y) + 200*im(p)*re(p) + 4800*im(y)*re(y)) + \470 - 2400*im (y) - 100*im (p) + 100*re (p) + 1000*re(y) + 2400*re (y)/ *cos|------------------------------------------------------------------------------------------------------------------------------|| | re(p) | im(p) \ 2 /| \ 2 /| | re(p) | im(p) \ 2 /| \ 2 /| |- ----- + I*|- ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|- ----- + I*|- ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 5 \ 5 50 / 50 / \ 5 \ 5 50 / 50 /
$$\left(i \left(- \frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{im}{\left(p\right)}}{5}\right) - \frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{re}{\left(p\right)}}{5}\right) \left(i \left(\frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{im}{\left(p\right)}}{5}\right) + \frac{\sqrt[4]{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)}\right)^{2} + \left(100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(200 \operatorname{re}{\left(p\right)} \operatorname{im}{\left(p\right)} + 4800 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1000 \operatorname{im}{\left(y\right)},100 \left(\operatorname{re}{\left(p\right)}\right)^{2} + 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1000 \operatorname{re}{\left(y\right)} - 100 \left(\operatorname{im}{\left(p\right)}\right)^{2} - 2400 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 470 \right)}}{2} \right)}}{50} - \frac{\operatorname{re}{\left(p\right)}}{5}\right)$$
=
2 2 47 24*re (y) 2*re(y) 24*im (y) 2*I*im(y) 48*I*im(y)*re(y) - --- - --------- - ------- + --------- - --------- - ---------------- 250 25 5 25 5 25
$$- \frac{24 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{25} - \frac{48 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{25} - \frac{2 \operatorname{re}{\left(y\right)}}{5} + \frac{24 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{25} - \frac{2 i \operatorname{im}{\left(y\right)}}{5} - \frac{47}{250}$$
-47/250 - 24*re(y)^2/25 - 2*re(y)/5 + 24*im(y)^2/25 - 2*i*im(y)/5 - 48*i*im(y)*re(y)/25