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Question: How to collect exp(I*(Omega*t-k*x-z*k[1])) and exp(-I*(Omega*t-k*x-z*k[1]))

Question:How to collect exp(I*(Omega*t-k*x-z*k[1])) and exp(-I*(Omega*t-k*x-z*k[1]))

bashar27 55 Maple 18
collect
April 08 2022
1

restart;
H := a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1]));
I*(diff(H, z))+diff(H, x, x)+diff(H, t, t)+R*(H+conjugate(H))+R^2*(H+conjugate(H))*H;
value(%);
simplify(%);

> 

restart;
> 

H := a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1]));

a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1]))

> 

I*(diff(H, z))+diff(H, x, x)+diff(H, t, t)+R*(H+conjugate(H))+R^2*(H+conjugate(H))*H;

I*(I*a__1*k[1]*exp(I*(-Omega*t+k*x+z*k[1]))-I*a__2*k[1]*exp(-I*(-Omega*t+k*x+z*k[1])))-a__1*k^2*exp(I*(-Omega*t+k*x+z*k[1]))-a__2*k^2*exp(-I*(-Omega*t+k*x+z*k[1]))-a__1*Omega^2*exp(I*(-Omega*t+k*x+z*k[1]))-a__2*Omega^2*exp(-I*(-Omega*t+k*x+z*k[1]))+R*(a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1]))+conjugate(a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1]))))+R^2*(a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1]))+conjugate(a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1]))))*(a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1])))

> 

value(%);

I*(I*a__1*k[1]*exp(I*(-Omega*t+k*x+z*k[1]))-I*a__2*k[1]*exp(-I*(-Omega*t+k*x+z*k[1])))-a__1*k^2*exp(I*(-Omega*t+k*x+z*k[1]))-a__2*k^2*exp(-I*(-Omega*t+k*x+z*k[1]))-a__1*Omega^2*exp(I*(-Omega*t+k*x+z*k[1]))-a__2*Omega^2*exp(-I*(-Omega*t+k*x+z*k[1]))+R*(a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1]))+conjugate(a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1]))))+R^2*(a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1]))+conjugate(a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1]))))*(a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1])))

> 

simplify(%);

a__1^2*exp(-(2*I)*(Omega*t-k*x-z*k[1]))*R^2+2*a__1*a__2*R^2+a__2^2*exp((2*I)*(Omega*t-k*x-z*k[1]))*R^2-exp(-I*(Omega*t-k*x-z*k[1]))*a__1*k[1]+a__2*k[1]*exp(I*(Omega*t-k*x-z*k[1]))+a__1*exp(-I*(Omega*t-k*x-z*k[1]))*conjugate(a__1*exp(-I*(Omega*t-k*x-z*k[1]))+a__2*exp(I*(Omega*t-k*x-z*k[1])))*R^2+a__2*exp(I*(Omega*t-k*x-z*k[1]))*conjugate(a__1*exp(-I*(Omega*t-k*x-z*k[1]))+a__2*exp(I*(Omega*t-k*x-z*k[1])))*R^2-a__1*Omega^2*exp(-I*(Omega*t-k*x-z*k[1]))-a__1*k^2*exp(-I*(Omega*t-k*x-z*k[1]))-a__2*Omega^2*exp(I*(Omega*t-k*x-z*k[1]))-a__2*k^2*exp(I*(Omega*t-k*x-z*k[1]))+R*a__1*exp(-I*(Omega*t-k*x-z*k[1]))+R*a__2*exp(I*(Omega*t-k*x-z*k[1]))+R*conjugate(a__1*exp(-I*(Omega*t-k*x-z*k[1]))+a__2*exp(I*(Omega*t-k*x-z*k[1])))

> 

 

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