This work examines the symmetry of the complex modified KdV (cmKdV) equation. We use the Lie symmetry approach to the hydrodynamic-like system generated from the cmKdV equation via the Madelung transformation. A thorough set of local point symmetries is defined. Optimal systems up to four dimensions are constructed using the adjoint transformation and the admitted Lie algebra invariants. A one-dimensional optimal system is utilized to obtain similarity reductions and invariant solutions, which are then graphically presented. Furthermore, we compute the governing system`s conservation rules using the multiplier approach and the nonlinear self-adjointness.