How to solve 3 linear first order equations using diagonalization when the eigenvalues are complex: An example

Question

Given the following set of equations \begin{equation} \dot{X}(t) = M X(t) = \begin{pmatrix} -A/2 & 0 & 0\\ 0 & - A/2 & B\\ 0 & -B & -A \end{pmatrix} X(t) \end{equation} where $A$ and $B$ are constants, and $X(t) = \begin{pmatrix} x_1(t)\\ x_2(t)\\ x_3(t) \end{pmatrix}$. How can this system of equations be solved using diagonalization of $M$, since the eigenvalues of $M$ turn out to be complex, $m_1 = -A/2$, $m_{\pm} = -3A/4 \pm i K.$ where $K = \sqrt{B^2 - (A/4)^2}$. Assume the initial conditions as $x_1^0,x_2^0,x_3^0$.