How to use phasor method for analyzing electrical circuits when current has DC components So let's say that we have a electrical circuit with a current source that is sinusoidal, but has DC offsets. How then do we convert this $i(t)$ into phasor $I$? Or is this generally impossible?
 A: DC bias is $A e^{i\theta} e^{i\omega t} = A e^{i\cdot 0} e^{i\cdot 0 t} = A$, however, quoting this,

Phasors and Complex impedances are only relevant to sinusoidal sources.

A: If your source has both a sinusoidal component and a constant (DC) component, simply perform two separate analyses - a DC analysis and an AC analysis.
For the DC analysis, the sinusoidal component is zeroed and the (constant) voltages and currents are solved for (recall that capacitors are replaced with open circuit and inductors are replaced with wires).
For the AC analysis, the DC component is zeroed and the phasor voltages and currents are solved for.
The total solution is the DC solution plus the time domain AC solution (found by restoring the time variation to the phasors and taking the real part of the result).
This assumes the circuit is linear so that such a superposition is valid.
If the circuit is non-linear, a similar approach can be taken by linearizing the circuit about the DC operating point and understanding that the resulting AC analysis is valid only for small variations about the operating point (AC small signal analysis).
A: Phasors are a way to analyse linear circuits using fourier analusis for the input, so the output can be analysed per frequency component (definition of linear circuit). (see related answer)
Any (pure) DC component appears as a constant term (or bias term).
Each phasor represents only one frequency component $I(\omega)$
But one can also take limits when $\lim_{->0} \omega$ i.e the frequency of the signal is very low or close to zero.
