Compute the solution $\phi_t \overrightarrow x_0 = e^{At} \overrightarrow x_0$ to the system $x' = -x + 4y$ and $y' = -4x - y$

The characteristic equation i found is $\lambda^2 + 2\lambda + 17$...The eienvalues are -1+- 4i....can anyone help me to move forward since i do not know how to find the eigenvector from non real eigenvalues?