Imaginary

tap × i and watch the arrow. then tap it again.

multiplying by i turns any arrow a quarter turn: tap twice and 1 becomes −1, which is all i × i = −1 says

A complex number is a point on a plane: across is the real part, up is the imaginary part. Multiplying by i turns that point a quarter turn around zero and keeps its length. Two quarter turns point it the opposite way, which is multiplying by −1: so i × i = −1.

Concepts: geometry, symmetry.

An interactive you play with one thumb, on Wundr.