I am reading MIT PDF here: http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-ii-second-order-constant-coefficient-linear-equations/exponential-response/MIT18_03SCF11_s14_4btext.pdf
The 2nd question is
and the solution is :
My question is, how do they go from the complex form to the real form? Re(z), what is this operation.
Also, if the function had been a sin(t) instead of cos(t) in the ODE, then I would take Im(z), how do I do this operation aswell?
An example where that might apply is let's say x''+5'x+6x = sin(5t)