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Let z = x + iy be a complex number.
Let z = r {cos q + i sin q} be its polar form.
[2np + q is the general amplitude]

Since we are finding the qth roots of a complex number, z1/q should satisfy the equation xq = z which is an algebraic equation of degree q and should have exactly q roots.
where n = 0,1,2,3,........, q-1
By giving values for n = 0,1,2,3,........, q-1, we get q distinct qth roots of z.Cube roots of unity

where 2np + 0 is the general amplitude.


\The cube roots of unity are
which are usually denoted by 1, w, w2.
Note 1:

Note 2:


Note 3:


Note 4:

Fourth roots of unity






Note:



