The core principle of phasor representation is the application of Euler's formula to transform time-domain sinusoidal functions into stationary complex exponentials within the frequency domain, enabling linearization of differential equations governing steady-state systems. This formalism defines voltage and current as rotating vectors characterized by magnitude and phase angle relative to a reference frequency, strictly operating under the conditions that all signals share identical angular frequencies (ω) in stable states. As a fundamental method within electrical engineering and mathematical physics, it provides an unambiguous framework for analyzing linear time-invariant systems where transient behaviors have decayed.
Prerequisite chain context: requires Kirchhoff's Laws in Low-Frequency Circuit Theory.