root of unity

See heptadecagon for the real part of a 17th root of unity.

This follows immediately from the fact that is, by definition, an th root of unity.

Being aware of myself in all human bodies, is the root of unity".

This embedding can be defined over the field generated by the 15th roots of unity.

Sending a to a primitive root of unity gives an isomorphism between the two.

However, there are no primitive 3rd roots of unity in a real closed field.

Indeed, suppose that ω is a primitive 3rd root of unity.

Note that is also a square root of unity.

Let be the real subfield of where is a 7th-primitive root of unity.

The spins therefore take values in the form of complex roots of unity.