Complex Polar Coordinates in Electromagnetics

Abstract

The definition of a complex polar coordinate system that unifies complex distances and complex angles together with their relations with the real observation space is presented in this paper. Its utility is shown through some applications to electromagnetic problems: (i) new solutions are obtained from well-known solutions in real polar coordinates, (ii) the parameterization of the real space in terms of the complex polar coordinates helps to understand the physical behaviour of those solutions, and (iii) the results provide a better physical insight of the complex distances and angles.