Read the result
The roots all have modulus 1. Only the angle changes, stepping by 360/n degrees each time.
Complex numbers
Roots of Unity Visualiser
See the nth roots of unity as equally spaced points around the unit circle.
Formula
z_k = cos(2*pi*k/n) + i sin(2*pi*k/n)
Result
Worked substitution
Roots of unity divide the circle into equal angular steps.
Where it helps
This is the visual foundation for De Moivre's theorem, complex roots, and symmetric phasor patterns.
Common slip
n counts how many roots there are, not the final index. The labels run from 0 to n - 1.
Try it
Set n to 4, then 8. Notice how the old fourth roots remain in the eighth-root pattern.