How Do You Solve for C1 and C2 in Damped Simple Harmonic Motion?

[runevxii]

I'm having trouble with this problem. I want to get it into a form with cos but I'm stumped.
The solution for damped simple harmonic motion is given by
x = (e^(-rt/2m))(C_1*e^(iw't)+C_2*e^(-iwt))
If x = Acos phi at t = 0, find the values of C_1 and C_2 to show that x'=(approx) -w'Asinphi at t = 0 only if r/m is very small or phi =(approx) pi/2.

Where w = omega and phi = angle phi and i=complex variable x' = 1st derivative

Any ideas or help would be really appreciated.

 

[Astronuc]

exp (ix) = cos x + i sin x, and exp (-ix) = cos x - i sinx

Expand the exponentials and then rearrange the coefficents for cos x and i sinx.