In this book, all known electromagnetic laws are proven to derivable from the solution of a single quadratic equation. This governing equation, it is shown, generates precisely three complex fields in 4-space, but can itself be generated as a law of all even-dimensioned spaces in universes having "meaning," without need of a prior knowledge of physics. Provided for the first time are electromagnetic formulas applicable in a general Riemannian space: the fundamental field tensor with three complex components, the energy-momentum tensor and the force-power tensor. The Lorentz force, as currently known, is shown to be an approximate form of the derived Riemannian force-power tensor, which imbeds gravitational interactions inclusive of frame-dragging terms. Newly identified electro-gravitational interaction force and power-transfer mechanisms are provided as natural consequences of the reformulations.As a byproduct of the complex-field theory developed in this book, the mystery of missing magnetic monopoles in nature is fully resolved. Also clarified are classical duality, field superposition, and the origins of charge sign and chirality. The approach taken to include all spatial dimensionalities leads to the justifiable conclusion that infinitely many higher-dimensioned spaces likely exist, with their laws of operation able to be broadly generated from the material presented.