Dear Andre,
Interpretation of the eigensolution has been discussed many times on this forum, including a discussion of the scripts from the MATLAB Toolbox (github.com/OpenFAST/matlab-toolbox)–such as MBC3 and runCampbell–that can aid in the interpretation of the MATLAB eig() function. The derivation of the natural frequencies, damped frequencies, and damping ratios from real and imaginary components of the eigenvalues has been discussed explicitly, e.g. here, which is the approach used by MBC3.
Best regards,