5.4 Use of Complex Exponential Source
The complex-exponential-source technique is the conceptual bridge to the forthcoming phasor technique (which is ubiquitous in practice)
In AC steady-state circuit analysis, sinusoidal sources are mathematically related to complex exponential sources via Euler’s Equation: ejx = cos(x) + jsin(x)
(Euler’s Equation provides the mathematical bridge)
Any particular solution for exponential source(s) is also a complex exponential, and is much easier to determine than its sinusoidal counterpart¾in fact, it can be found using (complex) arithmetic alone!
Finally, the particular (trigonometric) solution for any AC circuit can be readily deduced from its complex exponential counterpart