The expressions of totally polarized light with circular and elliptical basic vectors are two of the approaches to characterize states of optical polarization. Based on the theory of polarization optics and Jones calculus, we derive two sets of fundamental formulae expressing the states of optical polarization exploiting circular and elliptical basic vectors, propose a way to describe simultaneously four physical parameters using two elements of an optical vector，and an approach of drawing complex optical vectors′s locuses. The first step of the approach is to turn the complex optical vector into the form of a sum of two row vectors, and then, to superpose the two ellipses drawn according to the two vectors, into the final ellipse. We assess the feasibility of the methods proposed here, exploiting some typical examples of states of optical polarization. The results show that the formulae derived here are correct and the methods proposed here are feasible.