Energy as a complex number
Equations of gravity and electromagnetism exhibit structural similarities. After a convertion of units, the pattern we see could be mathematically explained in terms of complex variables, this expression ends up capturing some aspects of both fields in a compact notation.
: energy,   
: mass,   
: speed of light,   
: complex unit,   
: charge,   
: vacuum permittivity,   
: universal gravitational constant
Classical mechanics
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:
Special Relativity
Consider a complex Momentum P
: mass energy contribution
: charge energy contribution
To write:
being:
Which points us to express magnetic phenomena in terms of P.
Electromagnetism
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.
References
3. Wikipedia, Gravitoelectromagnetism
4. Wikipedia, Minkowski metric
5. Wikipedia, Schwarzschild metric
6. Carlos Francisco Romero Madrid, Derivation of the Metric of Reissner-Nordström and Kerr-Newman Black Holes, 2018
7. Guansheng He, Exact Harmonic Metric for a Uniformly Moving Schwarzschild Black Hole Article in Communications in Theoretical Physics · January 2014 261016243
8. Richard A. Hutchin, A Natural Combination of Gravity and Electromagnetism, Journal of Modern Physics, 2015, 6, 749-757 2015.66080
9. Bahram Mashhoon, Gravitoelectromagnetism: A Brief Review 0311030
10. Athanasios Bakopoulos, Gravitoelectromagnetism: Basic principles, novel approaches and their application to Electromagnetism 1610.08357
This equation was first digitally written and cryptographically signed on Sep-04-2022 09:46:26 PM +UTC as shown in "decoded input data" in the "more details" section of the following link:
E = Y*(m + i*Q/(4*pi*e0*G)^(1/2))*C^2

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Marcelo Villarreal Fasanelli - emq.guy@gmail.com