Imaginary

multiply by i and the number spins a quarter turn. that’s all it ever was.

drag any number, then tap its ghost — watch it turn exactly that far, every time

A complex number is just a point with two coordinates, real and imaginary. Multiplying it by i does exactly one thing to that point: it turns the whole plane ninety degrees around the origin and changes nothing else — not the distance from the centre, not which numbers are still neighbours. Do it four times and you are back exactly where you started, because four right angles make a full circle. That is the entire content of i squared equals minus one: not a magic symbol, a quarter turn, twice.

Concepts: geometry, symmetry.

An interactive you play with one thumb, on Wundr.