By the method of subsection 5.1, we compute all the roots of unity:
For , we have the following roots:
The images in Gauss-Argand plane of the roots of unity are the vertices of a regular polygone inscribed in the unit circle.
By De Moivre's formula De Moivre's formula, the following holds:
An immediate consequence is as follows:
Now, let us see a nice application of these roots of unity.
An additional result of this example is the following: compute polar forms for the roots of . Theses roots have arguments , , and . They fit exactly the order of the roots given above.
Noah Dana-Picard 2007-12-24