What complex numbers are and what they are used for.
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When dealing with something oscillating, a number that records the characteristics of oscillation isn’t sufficient, because the underlying process that we observe as oscillating could be actually rotating. We need two perpendicular views of oscillation to fully describe a rotation. With only one view, there wouldn’t be enough data.
In other words, when you are not seeing something moving doesn’t mean it’s not moving. It could be it’s moving in another dimension.
Complex numbers are invented for this purpose. It separates the part of what we see from what is actually going on.
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