Applications of de moiver’s theorem:
That is a fundamental theorem and has several applications.
nth Roots of Unity
One most important application of De-Moivre's Theorem is in computing equation of nth powers in complex number. Consider x be the nth root of unity. Then
Sum of the Roots:
Hence the sum of the roots of unity is zero.
Product of the Roots:
If n is even 
If n is odd 
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Note :
- The points shown by n nth roots of unity are presented at the vertices of a regular polygon of n sides emblazoned in a unit circle having centre at the origin, one vertex of a polygon being on the positive real axis. Geometrically shown as follows.
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