Imaginary part of complex number (first post)

1. The problem statement, all variables and given/known data
C=A*e^(-i*wt)*sin(k*x); A,w,t,k,x are real numbers. Find imaginary part.


2. Relevant equations



3. The attempt at a solution
Im(C)=cos(wt)-i*sin(wt)
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

 

so then the imaginary party would be sin(wt)?

and what happens to the A in the function?

 

e^(-iwt)=cos(wt)-i*sin(wt) is how I think to the Euler formula...

then do i substitute it back into the original expression?

 

so...

C=A*cos(wt)*sin(kx)-i*A*sin(wt)*sin(kx)

Re(C)=A*cos(wt)*sin(kx)
and
Im(C)=-A*sin(wt)*sin(kx)

is this the proper solution?

And thanks dx

 

good stuff much appreciated dx