1. The problem statement, all variables and given/known data Given u(x,t) = sum( e^(-at/2)*cos(n*pi*x/2L) * Re[A_n*e^(i*w_n*t)+B_n*e^(-i*w_n*t)], and the boundary conditions u(-L)=u(L)=0 for all t; du/dt = 0 for all x at t = 0; u(x,t=0) = e^(-|x|/l) Find A_n and B_n. 2. Relevant equations N/A 3. The attempt at a solution I have attempted to turn the Real part into coefficients of cos and sin, i.e.: Re[A_n*e^(i*w_n*t)+B_n*e^(-i*w_n*t)] = C_n cos(w_n*t) + D_n sin (w_n*t) then taking advantage of cos orthogonality in x to get C and D. I can't think of how to turn C and D into A and B. So far I figured out that C is the real part of A+B, but I can't figure out how to get the imaginary parts of A and B from C and D. I'm sure it's simple, but I just can't seem to get it. Any help is appreciated.