rw
In AC circuit analysis, we use complex numbers (and complex exponentials) as a convenient way to represent sinusoidal voltages and currents. This makes the math easier because we can handle amplitude and phase information together.
When we use a complex exponential like Vke^(jωt) to represent a voltage, the real part of this expression, Re{Vke^(jωt)}, gives us the actual, physically measurable voltage waveform.
x(t) = A₁e^(j(ω₁t + φ₁)) + A₂e^(j(ω₂t + φ₂)) + ... + Aₙe^(j(ωₙt + φₙ))
-
A₁, A₂, ..., Aₙrepresent the amplitudes of each component. -
ω₁, ω₂, ..., ωₙrepresent the angular frequencies of each component (ω = 2πf, where f is the frequency in Hz). -
φ₁, φ₂, ..., φₙrepresent the phase shifts of each component. -
jis the imaginary unit (√-1). -
Notice it is j(wt + φ) and not jwt + φ.