  Two distinct systems of commutative complex numbers in n dimensions are
described, of polar and planar types. Exponential forms of n-complex numbers
are given in each case, which depend on geometric variables. Azimuthal angles,
which are cyclic variables, appear in these forms at the exponent, and this
leads to the concept of residue for path integrals of n-complex functions. The
exponential function of an n-complex number is expanded in terms of functions
called in this paper cosexponential functions, which are generalizations to n
dimensions of the circular and hyperbolic sine and cosine functions. The
factorization of n-complex polynomials is discussed.
