Question about complex frequencies

Hi!

I'm simulating a MEMS resonator using Thermoelasticity and an eigenfrequency study. As might be expected, I'm obtaining complex frequencies due to the damping.

I looked all over the forum and the answers about the meaning of the real and imaginary parts of the frequency are very confusing to me since nobody makes clear for what stands the real part of the frequency.
So, my question is, what means the real part? Is the undamped resonance frequency or the damped resonance frequency?
Is the imaginary part the damping ratio 'zeta', or the damping coefficient 'c' that is used with the critical damping to obtain the damping ratio?

Thanks for the help!