Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 12/(x+3)=-6/7
-
Ecuación (x-6)(4x-6)=0
-
Ecuación (x+7)^3=9*(x+7)
-
Ecuación z^2+z+1=0
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 7*x-1*y=0
- -9*x-1*y=6
- -2*x+2*y=4
-
Expresiones idénticas
- (log(y)+ uno)/y=c-log(x)
- ( logaritmo de (y) más 1) dividir por y es igual a c menos logaritmo de (x)
- ( logaritmo de (y) más uno) dividir por y es igual a c menos logaritmo de (x)
- logy+1/y=c-logx
- (log(y)+1) dividir por y=c-log(x)
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Expresiones semejantes
- log(y^3+5)/3=(c-log(x^3+5))/3
- (-3)*y^2/2+6*y=c-log(x^2+3)/2
- log(y^2+1)/2=c-log(x^2-1)/2
- (log(y)-1)/y=c-log(x)
- log(y)+1/y=1/x+log(x)
- (log(y)+1)/y=c+log(x)
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Expresiones con funciones
- Logaritmo log
- log(3)*27=x
- log(1)/9=2+x
- log(4/(7-x))/log(x^2)=11
- log(y+1)=Const-log(x-1)
- log(4*3^(x-1)-1)/log(3)=2*x-1
- Logaritmo log
- log(3)*27=x
- log(1)/9=2+x
- log(4/(7-x))/log(x^2)=11
- log(y+1)=Const-log(x-1)
- log(4*3^(x-1)-1)/log(3)=2*x-1
(log(y)+1)/y=c-log(x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
log(y) + 1
---------- = c - log(x)
y
$$\frac{\log{\left(y \right)} + 1}{y} = c - \log{\left(x \right)}$$
Solución detallada
Tenemos la ecuación
$$\frac{\log{\left(y \right)} + 1}{y} = c - \log{\left(x \right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$\log{\left(x \right)} = c - \frac{\log{\left(y \right)} + 1}{y}$$
Es la ecuación de la forma:
Por definición log
entonces
$$x = e^{\frac{c - \frac{\log{\left(y \right)} + 1}{y}}{1}}$$
simplificamos
$$x = e^{c - \frac{\log{\left(y \right)} + 1}{y}}$$
$$\frac{\log{\left(y \right)} + 1}{y} = c - \log{\left(x \right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$\log{\left(x \right)} = c - \frac{\log{\left(y \right)} + 1}{y}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$x = e^{\frac{c - \frac{\log{\left(y \right)} + 1}{y}}{1}}$$
simplificamos
$$x = e^{c - \frac{\log{\left(y \right)} + 1}{y}}$$
Gráfica
Respuesta rápida
[src]
re(y) im(y)*im(c*y) re(y)*re(c*y) arg(y)*im(y) log(|y|)*re(y) re(y) im(y)*im(c*y) re(y)*re(c*y) arg(y)*im(y) log(|y|)*re(y)
- --------------- + --------------- + --------------- - --------------- - --------------- - --------------- + --------------- + --------------- - --------------- - ---------------
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
/ im(y) im(y)*log(|y|) im(c*y)*re(y) arg(y)*re(y) im(y)*re(c*y) \ im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) / im(y) im(y)*log(|y|) im(c*y)*re(y) arg(y)*re(y) im(y)*re(c*y) \
x1 = cos|--------------- + --------------- + --------------- - --------------- - ---------------|*e + I*e *sin|--------------- + --------------- + --------------- - --------------- - ---------------|
| 2 2 2 2 2 2 2 2 2 2 | | 2 2 2 2 2 2 2 2 2 2 |
\im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y)/ \im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y)/
$$x_{1} = i e^{- \frac{\log{\left(\left|{y}\right| \right)} \operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{re}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{im}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} \sin{\left(\frac{\log{\left(\left|{y}\right| \right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(c y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)} + e^{- \frac{\log{\left(\left|{y}\right| \right)} \operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{re}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{im}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} \cos{\left(\frac{\log{\left(\left|{y}\right| \right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(c y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}$$
x1 = i*exp(-log(|y|)*re(y)/(re(y)^2 + im(y)^2) + re(y)*re(c*y)/(re(y)^2 + im(y)^2) - re(y)/(re(y)^2 + im(y)^2) + im(y)*im(c*y)/(re(y)^2 + im(y)^2) - im(y)*arg(y)/(re(y)^2 + im(y)^2))*sin(log(|y|)*im(y)/(re(y)^2 + im(y)^2) + re(y)*im(c*y)/(re(y)^2 + im(y)^2) - re(y)*arg(y)/(re(y)^2 + im(y)^2) - re(c*y)*im(y)/(re(y)^2 + im(y)^2) + im(y)/(re(y)^2 + im(y)^2)) + exp(-log(|y|)*re(y)/(re(y)^2 + im(y)^2) + re(y)*re(c*y)/(re(y)^2 + im(y)^2) - re(y)/(re(y)^2 + im(y)^2) + im(y)*im(c*y)/(re(y)^2 + im(y)^2) - im(y)*arg(y)/(re(y)^2 + im(y)^2))*cos(log(|y|)*im(y)/(re(y)^2 + im(y)^2) + re(y)*im(c*y)/(re(y)^2 + im(y)^2) - re(y)*arg(y)/(re(y)^2 + im(y)^2) - re(c*y)*im(y)/(re(y)^2 + im(y)^2) + im(y)/(re(y)^2 + im(y)^2))
Suma y producto de raíces
[src]
suma
re(y) im(y)*im(c*y) re(y)*re(c*y) arg(y)*im(y) log(|y|)*re(y) re(y) im(y)*im(c*y) re(y)*re(c*y) arg(y)*im(y) log(|y|)*re(y)
- --------------- + --------------- + --------------- - --------------- - --------------- - --------------- + --------------- + --------------- - --------------- - ---------------
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
/ im(y) im(y)*log(|y|) im(c*y)*re(y) arg(y)*re(y) im(y)*re(c*y) \ im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) / im(y) im(y)*log(|y|) im(c*y)*re(y) arg(y)*re(y) im(y)*re(c*y) \
cos|--------------- + --------------- + --------------- - --------------- - ---------------|*e + I*e *sin|--------------- + --------------- + --------------- - --------------- - ---------------|
| 2 2 2 2 2 2 2 2 2 2 | | 2 2 2 2 2 2 2 2 2 2 |
\im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y)/ \im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y)/
$$i e^{- \frac{\log{\left(\left|{y}\right| \right)} \operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{re}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{im}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} \sin{\left(\frac{\log{\left(\left|{y}\right| \right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(c y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)} + e^{- \frac{\log{\left(\left|{y}\right| \right)} \operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{re}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{im}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} \cos{\left(\frac{\log{\left(\left|{y}\right| \right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(c y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}$$
=
re(y) im(y)*im(c*y) re(y)*re(c*y) arg(y)*im(y) log(|y|)*re(y) re(y) im(y)*im(c*y) re(y)*re(c*y) arg(y)*im(y) log(|y|)*re(y)
- --------------- + --------------- + --------------- - --------------- - --------------- - --------------- + --------------- + --------------- - --------------- - ---------------
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
/ im(y) im(y)*log(|y|) im(c*y)*re(y) arg(y)*re(y) im(y)*re(c*y) \ im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) / im(y) im(y)*log(|y|) im(c*y)*re(y) arg(y)*re(y) im(y)*re(c*y) \
cos|--------------- + --------------- + --------------- - --------------- - ---------------|*e + I*e *sin|--------------- + --------------- + --------------- - --------------- - ---------------|
| 2 2 2 2 2 2 2 2 2 2 | | 2 2 2 2 2 2 2 2 2 2 |
\im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y)/ \im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y)/
$$i e^{- \frac{\log{\left(\left|{y}\right| \right)} \operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{re}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{im}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} \sin{\left(\frac{\log{\left(\left|{y}\right| \right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(c y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)} + e^{- \frac{\log{\left(\left|{y}\right| \right)} \operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{re}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{im}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} \cos{\left(\frac{\log{\left(\left|{y}\right| \right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(c y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}$$
producto
re(y) im(y)*im(c*y) re(y)*re(c*y) arg(y)*im(y) log(|y|)*re(y) re(y) im(y)*im(c*y) re(y)*re(c*y) arg(y)*im(y) log(|y|)*re(y)
- --------------- + --------------- + --------------- - --------------- - --------------- - --------------- + --------------- + --------------- - --------------- - ---------------
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
/ im(y) im(y)*log(|y|) im(c*y)*re(y) arg(y)*re(y) im(y)*re(c*y) \ im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) / im(y) im(y)*log(|y|) im(c*y)*re(y) arg(y)*re(y) im(y)*re(c*y) \
cos|--------------- + --------------- + --------------- - --------------- - ---------------|*e + I*e *sin|--------------- + --------------- + --------------- - --------------- - ---------------|
| 2 2 2 2 2 2 2 2 2 2 | | 2 2 2 2 2 2 2 2 2 2 |
\im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y)/ \im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y) im (y) + re (y)/
$$i e^{- \frac{\log{\left(\left|{y}\right| \right)} \operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{re}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{im}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} \sin{\left(\frac{\log{\left(\left|{y}\right| \right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(c y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)} + e^{- \frac{\log{\left(\left|{y}\right| \right)} \operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{re}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{im}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} \cos{\left(\frac{\log{\left(\left|{y}\right| \right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(c y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}$$
=
-re(y) + im(y)*im(c*y) + re(y)*re(c*y) - arg(y)*im(y) - log(|y|)*re(y) I*(im(y)*log(|y|) + im(c*y)*re(y) - arg(y)*re(y) - im(y)*re(c*y) + im(y))
---------------------------------------------------------------------- + -------------------------------------------------------------------------
2 2 2 2
im (y) + re (y) im (y) + re (y)
e
$$e^{\frac{- \log{\left(\left|{y}\right| \right)} \operatorname{re}{\left(y\right)} + \operatorname{re}{\left(y\right)} \operatorname{re}{\left(c y\right)} - \operatorname{re}{\left(y\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(c y\right)} - \operatorname{im}{\left(y\right)} \arg{\left(y \right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{i \left(\log{\left(\left|{y}\right| \right)} \operatorname{im}{\left(y\right)} + \operatorname{re}{\left(y\right)} \operatorname{im}{\left(c y\right)} - \operatorname{re}{\left(y\right)} \arg{\left(y \right)} - \operatorname{re}{\left(c y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y\right)}\right)}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}}$$
exp((-re(y) + im(y)*im(c*y) + re(y)*re(c*y) - arg(y)*im(y) - log(|y|)*re(y))/(im(y)^2 + re(y)^2) + i*(im(y)*log(|y|) + im(c*y)*re(y) - arg(y)*re(y) - im(y)*re(c*y) + im(y))/(im(y)^2 + re(y)^2))