Question: simplify the multiply exponential term

i am looking for simplify this type of simplifying assume beta is Real and there is any stuf package for working with complex and conjugate automaticaly

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restart

with(inttrans)

with(PDEtools)

with(DEtools)

with(DifferentialAlgebra)

"with(Student[ODEs][Solve]): "

with(IntegrationTools)

with(inttrans)

with(PDEtools)

with(Physics)

with(PolynomialTools)

with(RootFinding)

with(SolveTools)

with(LinearAlgebra)

with(sumtools)

declare(u(x, t), conjugate(u(x, t)))

u(x, t)*`will now be displayed as`*u

(1)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(2)

B__0 := I*G(x)^3*conjugate(G(x))^2+(2*I)*G(x)^2*(diff(G(x), x))+(2*I)*(diff(G(x), x))*G(x)*conjugate(G(x))

I*G(x)^3*conjugate(G(x))^2+(2*I)*G(x)^2*(diff(G(x), x))+(2*I)*(diff(G(x), x))*G(x)*conjugate(G(x))

(3)

"G(x):=beta*exp(I*x) "

proc (x) options operator, arrow, function_assign; Physics:-`*`(beta, exp(Physics:-`*`(I, x))) end proc

(4)

R__0 := diff(G(x), `$`(x, 2))

-beta*exp(I*x)

(5)

B__0

I*beta^3*(exp(I*x))^3*conjugate(beta*exp(I*x))^2-2*beta^3*(exp(I*x))^3-2*beta^2*(exp(I*x))^2*conjugate(beta*exp(I*x))

(6)

"#`B__0 `must equal to (I*beta^(5)*exp(I*x)) after simplify betwen expresion  what code need i don't know"?""

B1 := laplace(B__0, t, s)

(-2*beta^2*exp((2*I)*x)*conjugate(beta*exp(I*x))+(I*conjugate(beta*exp(I*x))+1+I)*(conjugate(beta*exp(I*x))+(-1+I))*exp((3*I)*x)*beta^3)/s

(7)

R1 := laplace(R__0, t, s)

-beta*exp(I*x)/s

(8)

B2 := invlaplace(B1/s, s, t)

(-2*beta^2*exp((2*I)*x)*conjugate(beta*exp(I*x))+(I*conjugate(beta*exp(I*x))+1+I)*(conjugate(beta*exp(I*x))+(-1+I))*exp((3*I)*x)*beta^3)*t

(9)

R2 := invlaplace(R1/s, s, t)

-beta*exp(I*x)*t

(10)

Sol := B2+R2

(-2*beta^2*exp((2*I)*x)*conjugate(beta*exp(I*x))+(I*conjugate(beta*exp(I*x))+1+I)*(conjugate(beta*exp(I*x))+(-1+I))*exp((3*I)*x)*beta^3)*t-beta*exp(I*x)*t

(11)

simplify((-2*beta^2*exp((2*I)*x)*conjugate(beta*exp(I*x))+(I*conjugate(beta*exp(I*x))+1+I)*(conjugate(beta*exp(I*x))+(-1+I))*exp((3*I)*x)*beta^3)*t-beta*exp(I*x)*t)

(I*exp((3*I)*x)*conjugate(beta*exp(I*x))^2*beta^2-2*exp((2*I)*x)*conjugate(beta*exp(I*x))*beta-2*exp((3*I)*x)*beta^2-exp(I*x))*beta*t

(12)

expand((I*exp((3*I)*x)*conjugate(beta*exp(I*x))^2*beta^2-2*exp((2*I)*x)*conjugate(beta*exp(I*x))*beta-2*exp((3*I)*x)*beta^2-exp(I*x))*beta*t)

I*beta^3*t*(exp(I*x))^3*conjugate(beta)^2*(exp(-I*conjugate(x)))^2-2*t*beta^2*(exp(I*x))^2*conjugate(beta)*exp(-I*conjugate(x))-2*t*(exp(I*x))^3*beta^3-beta*exp(I*x)*t

(13)
 

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