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AC circuits - Complex vs Ordinary notation

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When doing calculations on AC circuits, what is in your opinion the best notation? Here they mostly use complex notation. For example: V(t) = Vmaxeiωt. In US textbooks (at the non-EE level), they only use ordinary notation. Example: V(t) = Vmaxcos(ωt).

I have a feeling that complex notation is faster, but also less intuitive. So which should I learn properly (and no, I don't want to be an expert in both)? The quicker complex notation, or the much more intuitively pleasing ordinary notation?

BTW: I don't study electrical engineering, but engineering physics.

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