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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