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We show an application of four states algebraic invariants to the extraction of the main optical properties of anisotropic semiconductor thin nanowires such as the complex propagation constant of the guided modes and the reflectivity at the waveguide terminations. In order to provide a numerical example, we calculate the modal and threshold gains for the first few guided modes. This has been done in conjunction with the use of a full-wave finite-element method simulator without the isotropic approximation of passive GaN. Moreover, the device has been directly analyzed in his active state, i.e., with a complex dielectric tensor: in principle, a rigorous complex resonance for simultaneously calculating the lasing frequency and the threshold gain may be performed.