# The effects of particles with complex electromagnetic charges on current physics

I've just had a crazy idea, and I need some input on it. It is entirely theoretical, and maybe I don't understand much about how electromagnetism works, but what if particles could have complex charges?

By this, I mean having a charge with "real" and "imaginary" properties. Eg. $$3-i$$ or $$\sqrt 2i$$.

First, let's define a particle $$q$$ with a charge of $$i\cdot e$$, and a particle $$p$$ with charge $$i^3\cdot e$$, or $$-i\cdot e$$.

Initially, it becomes apparent that when two $$q$$ particles or two $$p$$ particles interact, they attract each other, while a $$q$$ and a $$p$$ particle will repell each other. This is because in Coulomb's Law, $$F=k_e\frac{q_1q_2}{r^2}$$, when using purely imaginary values ($$i$$,$$-i$$) for $$q_1$$ and $$q_2$$, $$F$$ is positive when the charges are like-signed, and negative when they are different.

So what would happen if a particle with a real charge interacted with a particle with an imaginary charge? $$F$$ would have an imaginary value. If we use a particle with a complex charge, $$F$$ would be complex.

What kind of effects would we see if $$F$$ was imaginary or complex? Am I completely wrong in how electromagnetism works? Is "imaginary" or complex charge already a thing, and I've got it all wrong?