Monday, 13 August 2018

circuit analysis - Why use complex numbers to represent amplitude and phase of AC


Why is it that in AC circuits, sine waves are represented as a complex number in polar form? I don't logically understand from a physical perspective why there is an imaginary part at all. Is it purely from a mathematical point of view to make the analysis of circuits easier?



Answer



Quote: "Is it purely from a mathematical point of view to make the analysis of circuits easier?"


I am not sure if this part of the question was answered already sufficiently. Therefore: Yes - using complex mathematics for describing sinusoidal signals has no direct physical relevance. It is just to "make analyses easier".


As an example: Introducing Euler`s famous formula for sinus signals into the Fourier series leads to negative frequencies (symmetrical to positive frequencies). Hence, the question arises: Do negative frequencies exist in reality? The answer is NO! It is just a helpful mathematical tool.


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