When you find the eigenvalues $\lambda_n$ and corresponding eigenvectors $u_n$, some of them might be pairs of complex-conjugated eigenvectors $u_n=v_n\pm iw_n$ that correspond to complex-conjugated eigenvalues $\lambda_n=a_n\pm ib_n$.
In general, the modes associated with an eigenvalue and its eigenvector can be found as
Now for the case of complex-conjugated pairs of eigenvalues and vectors, choose only one pair of them and substitute them in the above relation. For instance, let's take
Notice that you could just as well choose the eigenvalue and vector with the "$-$" instead of the "$+$". Then plugging them in the relation for the mode $x_n(t)$ and simplifying (use Euler's formula for complex numbers and do some algebra) you find that
In this way, you've decomposed the mode into its real and imaginary parts. For a linear eigenvalue problem, both the real and the imaginary part are each real solutions of the problem; so you find two real solutions that represent real displacement modes of your structure. You should redo the simplifying in the above relation, just to be sure I haven't missed anything there!