So I have a general understanding of how to do these types of problems but I do not know how to get rid of the complex numbers. I found that the eigenvalues are 3i and -3i and the eigenvectors are [(-2/5 + 1/5 i), (1)] and [(-2/5 - 1/5 i), (1)].
The general equation would be v1*c1*cos(3t) + v2*c2*sin(3t) where I would then attempt to find the constants, however, when multiplying the vectors, more complex numbers are introduced and my answer must be real only.
How do I isolate the real part only?