Constructing three and higher n-dimensional complex number spherical and Cartesian coordinate systems based on rotation factors

Based on the set of real numbers and the set of rotation factors, the constructions of three and higher n-dimensional complex number spherical coordinate systems are realized. The projections of complex numbers or position vectors from four-dimensional space to three-dimensional space as well as from a higher n-dimensional space to a lower dimensional space are conceived. The projections are consistent throughout regardless of the dimensional levels and the generalization of the n-dimensional coordinate systems are achieved with n=2 for two-dimensional plane, n=3 for three-dimensional space, n=4 for four-dimensions and so on. The generalization of transformation to n-dimensional Cartesian coordinate systems from the spherical systems are obtained. The rotation operations in the n-dimensional complex number spherical coordinate systems are succinct and efficient, and the results can be transformed back to Cartesian coordinate systems, and vice versa.