Complex Energy Framework: Matter as E = pc + imc², Antimatter as E* = pc − imc², and the Derivation of Einstein's Energy-Momentum Relation

This paper extends the Force Impedance Model (Abdullah Baran, 2026) by developing the complex energy framework for matter and antimatter. The impedance model places kinetic energy on the real axis and rest energy on the imaginary axis: E = pc + i.mc². The complex conjugate E* = pc - i.mc² is identified as the natural representation of antimatter, corresponding to time reversal in the complex plane. The product E times E* yields (pc)² + (mc²)² directly, recovering Einstein's energy-momentum relation without external postulates. The framework also shows that rest energy E = i.mc² is purely imaginary, that photons carry no imaginary component, and that matter-antimatter annihilation corresponds algebraically to the cancellation of imaginary layers. All results follow from the impedance model's core axiom: balanced forces are rotated to the imaginary axis, not discarded.