Complex numbers · manipulative

The nth roots of unity

The equation zⁿ = 1 has exactly n solutions on the unit circle. Scrub k to walk from one root to the next by a fixed rotation of 2π/n.

z = 1 (k=0) other roots current k
5
0

Scrub k · each step is a rotate by 2π/n · scroll zoom · pan

Formula

All n roots