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Question: simplify the multiply exponential term

Question:simplify the multiply exponential term

salim-barzani 1555 Maple 2021
complex simplify assumptions conjugate assume
July 28 2024
0

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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NULL
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restart
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with(inttrans)
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with(PDEtools)
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with(DEtools)
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with(DifferentialAlgebra)
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"with(Student[ODEs][Solve]): "
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with(IntegrationTools)
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with(inttrans)
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with(PDEtools)
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with(Physics)
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with(PolynomialTools)
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with(RootFinding)
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with(SolveTools)
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with(LinearAlgebra)
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with(sumtools)
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declare(u(x, t), conjugate(u(x, t)))

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

 (1)
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undeclare(prime)

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

 (2)
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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)
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"G(x):=beta*exp(I*x) "

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

 (4)
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R__0 := diff(G(x), `$`(x, 2))

-beta*exp(I*x)

 (5)
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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)
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"#`B__0 `must equal to (I*beta^(5)*exp(I*x)) after simplify betwen expresion what code need i don't know"?""
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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)
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R1 := laplace(R__0, t, s)

-beta*exp(I*x)/s

 (8)
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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)
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R2 := invlaplace(R1/s, s, t)

-beta*exp(I*x)*t

 (10)
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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)
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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)
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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)
 

NULL

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