Cube Roots of Unity
Let z is the cube of unity, such that
either z - 1 = 0
z = 1
and are the cube roots of unity.
Properties of Cube Roots of Unity
P-1 One of the complex cube root of unity is real (i.e. 1) and the other two are conjugate complex of each other.
Sum of all cube roots of unity i ZERO i.e. 1+
Product of cube roots of unity is UNITY i.e.
P-2 Each Complex Cube root of unity is square of other.
P-3 Each complex Cube root of unity is reciprocal of each other
P-4 If a is any +iv number, then has roots
If a is any -iv number, then has roots
Geometrical Interpretation of Cube Roots of Unity