Given that Coulomb's inverse-square law [1] takes the form of Newton's law of universal gravitation [2] if we write:

It seems reasonable to explore the use of complex numbers, as a data structure, to treat electrostatics in a gravitational context.

Given the assumption:

Mass would be:

A complex gravitational potential defined as:

would hold enouh information to describe the classical static interaction with a different body. Which could provide a framework to justify why we don't seem to messure direct attraction/repulsion between mass and charge, since the representation of this interaction is caught in the imaginary part of:

Consider a complex Momentum P

To write:

being:

Which suggests that magnetic forces could be expressed in terms of P.

The description of Gravitoelectromagnetism [3] already gives us a good picture of the pattern. Converting Coloumbs into Kilograms using the following convertion factor, and allowing variables to be complex:

The full set of equations could be written as:

Subscripts m and e, refer to massive and electric quantities.

A complex number seems to be a suitable data structure to hold information about energy for certain calculations. Schrodinger equation, already deals with complex numbers, perhaps it is describing something similar. The energy of a photon would be a complex number too, just as the energy of an electron, making the absortion/emmision of a photon, comprehensible in terms of energy flow.

The study of a complex metric tensor, as the result of expressing it in terms of a complex potential, is left out of this document, and would be the subject of a second document.

Schwarzschild radius would be a complex number, which suggests that a change in the frame of reference could allow us to express the metric in terms of real numbers, forcing us to rotate, in the complex sense, the 4 momentum of a test particle, which would make it look with a different mass/charge distribution, even with negative mass, which in turn suggests that mass could be a relative quantity.