Sr Examen
Otras calculadoras
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¿Cómo usar?
- La ecuación:
-
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
-
Ecuación x(x^2+2x+1)=6(x+1)
-
Ecuación 4x+1=-3x+15
- Ecuación (3x−36)⋅(x+8)=0
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
-
Expresiones idénticas
- -log(y- cuatro)=Const+log(x^ dos + uno)
- menos logaritmo de (y menos 4) es igual a Const más logaritmo de (x al cuadrado más 1)
- menos logaritmo de (y menos cuatro) es igual a Const más logaritmo de (x en el grado dos más uno)
- -log(y-4)=Const+log(x2+1)
- -logy-4=Const+logx2+1
- -log(y-4)=Const+log(x²+1)
- -log(y-4)=Const+log(x en el grado 2+1)
- -logy-4=Const+logx^2+1
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Expresiones semejantes
- -log(y+4)=Const+log(x^2+1)
- -log(y-4)=Const-log(x^2+1)
- -log(y-4)=Const+log(x^2-1)
- log(y-4)=Const+log(x^2+1)
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Expresiones con funciones
- Logaritmo log
- log(x+1)=2*(x-2)^2
- log1÷2(x^2+4x-5)=-4
- log((2,2)+log(3,3+x))=0
- log(2/3)=(x*x-16)
- log(8)*x=2+x
- Logaritmo log
- log(x+1)=2*(x-2)^2
- log1÷2(x^2+4x-5)=-4
- log((2,2)+log(3,3+x))=0
- log(2/3)=(x*x-16)
- log(8)*x=2+x
-log(y-4)=Const+log(x^2+1) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 \ -log(y - 4) = c + log\x + 1/
$$- \log{\left(y - 4 \right)} = c + \log{\left(x^{2} + 1 \right)}$$
Gráfica
Respuesta rápida
[src]
_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / / -c \ / -c \ / -c \ / -c \\\ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / / -c \ / -c \ / -c \ / -c \\\
/ 2 2 | |/ re(c) re(c) \ | e | / re(c) re(c)\ | e | / re(c) re(c)\ | e | / re(c) re(c) \ | e ||| / 2 2 | |/ re(c) re(c) \ | e | / re(c) re(c)\ | e | / re(c) re(c)\ | e | / re(c) re(c) \ | e |||
/ / / -c \ / -c \\ / / -c \ / -c \\ |atan2|\- (-4 + re(y))*e *sin(im(c)) - cos(im(c))*e *im(y)/*re|------| + \1 + e *im(y)*sin(im(c)) - (-4 + re(y))*cos(im(c))*e /*im|------|, \1 + e *im(y)*sin(im(c)) - (-4 + re(y))*cos(im(c))*e /*re|------| - \- (-4 + re(y))*e *sin(im(c)) - cos(im(c))*e *im(y)/*im|------||| / / / -c \ / -c \\ / / -c \ / -c \\ |atan2|\- (-4 + re(y))*e *sin(im(c)) - cos(im(c))*e *im(y)/*re|------| + \1 + e *im(y)*sin(im(c)) - (-4 + re(y))*cos(im(c))*e /*im|------|, \1 + e *im(y)*sin(im(c)) - (-4 + re(y))*cos(im(c))*e /*re|------| - \- (-4 + re(y))*e *sin(im(c)) - cos(im(c))*e *im(y)/*im|------|||
/ |/ re(c) re(c) \ | e | / re(c) re(c)\ | e || |/ re(c) re(c)\ | e | / re(c) re(c) \ | e || | \ \-4 + y/ \-4 + y/ \-4 + y/ \-4 + y//| / |/ re(c) re(c) \ | e | / re(c) re(c)\ | e || |/ re(c) re(c)\ | e | / re(c) re(c) \ | e || | \ \-4 + y/ \-4 + y/ \-4 + y/ \-4 + y//|
x1 = 4 / |\- (-4 + re(y))*e *sin(im(c)) - cos(im(c))*e *im(y)/*re|------| + \1 + e *im(y)*sin(im(c)) - (-4 + re(y))*cos(im(c))*e /*im|------|| + |\1 + e *im(y)*sin(im(c)) - (-4 + re(y))*cos(im(c))*e /*re|------| - \- (-4 + re(y))*e *sin(im(c)) - cos(im(c))*e *im(y)/*im|------|| *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*4 / |\- (-4 + re(y))*e *sin(im(c)) - cos(im(c))*e *im(y)/*re|------| + \1 + e *im(y)*sin(im(c)) - (-4 + re(y))*cos(im(c))*e /*im|------|| + |\1 + e *im(y)*sin(im(c)) - (-4 + re(y))*cos(im(c))*e /*re|------| - \- (-4 + re(y))*e *sin(im(c)) - cos(im(c))*e *im(y)/*im|------|| *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\/ \ \-4 + y/ \-4 + y// \ \-4 + y/ \-4 + y// \ 2 / \/ \ \-4 + y/ \-4 + y// \ \-4 + y/ \-4 + y// \ 2 /
$$x_{1} = i \sqrt[4]{\left(\left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)} + \left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 1\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)}\right)^{2} + \left(- \left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)} + \left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 1\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)} + \left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 1\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)},- \left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)} + \left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 1\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)} + \left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 1\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)}\right)^{2} + \left(- \left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)} + \left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 1\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)} + \left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 1\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)},- \left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)} + \left(- \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 1\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)} \right)}}{2} \right)}$$
_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / / -c \ / -c \ / -c \ / -c \\\ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / / -c \ / -c \ / -c \ / -c \\\
/ 2 2 | | / re(c) re(c) \ | e | / re(c) re(c) \ | e | / re(c) re(c) \ | e | / re(c) re(c) \ | e ||| / 2 2 | | / re(c) re(c) \ | e | / re(c) re(c) \ | e | / re(c) re(c) \ | e | / re(c) re(c) \ | e |||
/ / / -c \ / -c \\ / / -c \ / -c \\ |atan2|- \(-4 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/*re|------| - \-1 + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))/*im|------|, \(-4 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/*im|------| - \-1 + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))/*re|------||| / / / -c \ / -c \\ / / -c \ / -c \\ |atan2|- \(-4 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/*re|------| - \-1 + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))/*im|------|, \(-4 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/*im|------| - \-1 + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))/*re|------|||
/ |/ re(c) re(c) \ | e | / re(c) re(c) \ | e || | / re(c) re(c) \ | e | / re(c) re(c) \ | e || | \ \-4 + y/ \-4 + y/ \-4 + y/ \-4 + y//| / |/ re(c) re(c) \ | e | / re(c) re(c) \ | e || | / re(c) re(c) \ | e | / re(c) re(c) \ | e || | \ \-4 + y/ \-4 + y/ \-4 + y/ \-4 + y//|
x2 = - 4 / |\(-4 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/*im|------| - \-1 + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))/*re|------|| + |- \(-4 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/*re|------| - \-1 + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))/*im|------|| *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I*4 / |\(-4 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/*im|------| - \-1 + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))/*re|------|| + |- \(-4 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/*re|------| - \-1 + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))/*im|------|| *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\/ \ \-4 + y/ \-4 + y// \ \-4 + y/ \-4 + y// \ 2 / \/ \ \-4 + y/ \-4 + y// \ \-4 + y/ \-4 + y// \ 2 /
$$x_{2} = - i \sqrt[4]{\left(- \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)} - \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)}\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)} - \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)} - \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)},\left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)} - \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)} \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)} - \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)}\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)} - \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)} - \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)},\left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(\frac{e^{- c}}{y - 4}\right)} - \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1\right) \operatorname{re}{\left(\frac{e^{- c}}{y - 4}\right)} \right)}}{2} \right)}$$
x2 = -i*((-((re(y) - 4)*exp(re(c))*sin(im(c)) + exp(re(c))*cos(im(c))*im(y))*re(exp(-c)/(y - 4)) - ((re(y) - 4)*exp(re(c))*cos(im(c)) - exp(re(c))*sin(im(c))*im(y) - 1)*im(exp(-c)/(y - 4)))^2 + (((re(y) - 4)*exp(re(c))*sin(im(c)) + exp(re(c))*cos(im(c))*im(y))*im(exp(-c)/(y - 4)) - ((re(y) - 4)*exp(re(c))*cos(im(c)) - exp(re(c))*sin(im(c))*im(y) - 1)*re(exp(-c)/(y - 4)))^2)^(1/4)*sin(atan2(-((re(y) - 4)*exp(re(c))*sin(im(c)) + exp(re(c))*cos(im(c))*im(y))*re(exp(-c)/(y - 4)) - ((re(y) - 4)*exp(re(c))*cos(im(c)) - exp(re(c))*sin(im(c))*im(y) - 1)*im(exp(-c)/(y - 4), ((re(y) - 4)*exp(re(c))*sin(im(c)) + exp(re(c))*cos(im(c))*im(y))*im(exp(-c)/(y - 4)) - ((re(y) - 4)*exp(re(c))*cos(im(c)) - exp(re(c))*sin(im(c))*im(y) - 1)*re(exp(-c)/(y - 4)))/2) - ((-((re(y) - 4)*exp(re(c))*sin(im(c)) + exp(re(c))*cos(im(c))*im(y))*re(exp(-c)/(y - 4)) - ((re(y) - 4)*exp(re(c))*cos(im(c)) - exp(re(c))*sin(im(c))*im(y) - 1)*im(exp(-c)/(y - 4)))^2 + (((re(y) - 4)*exp(re(c))*sin(im(c)) + exp(re(c))*cos(im(c))*im(y))*im(exp(-c)/(y - 4)) - ((re(y) - 4)*exp(re(c))*cos(im(c)) - exp(re(c))*sin(im(c))*im(y) - 1)*re(exp(-c)/(y - 4)))^2)^(1/4)*cos(atan2(-((re(y) - 4)*exp(re(c))*sin(im(c)) + exp(re(c))*cos(im(c))*im(y))*re(exp(-c)/(y - 4)) - ((re(y) - 4)*exp(re(c))*cos(im(c)) - exp(re(c))*sin(im(c))*im(y) - 1)*im(exp(-c)/(y - 4)), ((re(y) - 4)*exp(re(c))*sin(im(c)) + exp(re(c))*cos(im(c))*im(y))*im(exp(-c)/(y - 4)) - ((re(y) - 4)*exp(re(c))*cos(im(c)) - exp(re(c))*sin(im(c))*im(y) - 1)*re(exp(-c)/(y - 4)))/2))