Argand plane · manipulative

What multiplication actually does

Drag the two points. Every complex multiplication is a rotate-and-scale: lengths multiply, angles add.

z₁ z₂ z₁z₂
Set Arg(z₂)
Drag points · scroll zoom · drag background to pan

The two numbers

Show polar form
length ∠ angle, instead of a + bi
Show the product
reveal z₁ × z₂, worked out

Working