  Being inspired by phasor analysis in linear circuit theory, and its algebraic
counterpart - the AC-(operational)-calculus for sinusoids developed by W.
Marten and W. Mathis - we define a complex structure on several spaces of
real-valued elementary functions. This is used to algebraize inhomogeneous
linear ordinary differential equations with inhomogenities stemming from these
spaces. Thus we deduce an effective method to calculate particular solutions of
these ODEs in a purely algebraic way.
