The paper is concerned with the solution of linear systems with non- singular complex matrices. A unified framework is presented from which various conjugate gradient-like methods for solving the above described systems are derived. The considered methods include both well-known methods and some new variants of these methods. Namely, they include normal equation conjugate gradient method, conjugate residual method, complex orthomin, complex GMRES, biconjugate gradient method, biconjugate gradient squared method. The considered methods are tested on the set of four model problems consisting of three systems with non-symmetric non-Hermitian Toeplitz matrices and one system arising from discretization of the Helmholtz equation with a radiation boundary condition.