22 Jan 2021

Multiplication and Rotation

The following demo shows that multiplication (by a number distance one away from the origin) is the same as rotation.

Drag the red slider to rotate the point \(w\). Click and drag the point \(z\) to move it around.

The black \(+\) represents the point \(z\) rotated by \(a\) degrees, while the purple \(\times\) represents the product \(zw\). They’re the same!