The Importance of Real Orthonormal Eigenvectors in Classically Damped Systems

Question

The equations of motion of an $n$-degree-of-freedom linear dynamic system with viscous damping may be written in the form \begin{align} M \ddot x + C \dot x + K x = 0. \end{align} This system has been studied in the literature. If this system is classically damped, then the system has a complete set of real orthonormal eigenvectors namely the classical normal modes. I was wondering why having real eigenvectors is important. My major is not mechanical engineering, so I greatly appreciate any comment/insight. Thank you.