In the mathematical modeling of real-life applications, systems of equations with complex coefficients often arise. While many techniques of numerical linear algebra, e.g., Krylov-subspace methods, extend directly to the case of complex-valued matrices, some of the most effective preconditioning techniques and linear solvers are limited to the real-valued case. Here, we consider the extension of the popular algebraic multigrid method to such complex-valued systems. The choices for this generalization are motivated by classical multigrid considerations, evaluated with the tools of local Fourier analysis, and verified on a selection of problems related to real-life applications.