An interactive
Two shores, one rotation.
Complex numbers have a "real" part and an "imaginary" part, and we teach them as though one is solid and the other a mathematician's fiction. This is backwards. There is only one thing here — a rotation — and "real" and "imaginary" are just the two shadows it casts onto whichever axis you happen to be standing on. Walk ninety degrees and the shadows trade places: what looked imaginary becomes real, and the reverse. Nothing about the rotation changed. Only where you stood did. Every measurement you will ever make is a shadow like this — faithful to what's there, and never the whole of it. Drag the slider and watch.
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Your dial — you call this “real”
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The other shore — you call theirs “imaginary”
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