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
![932_Applications of de moiver theorem.png](https://www.expertsmind.com/../CMSImages/932_Applications of de moiver theorem.png)
![954_Applications of de moiver theorem1.png](https://www.expertsmind.com/../CMSImages/954_Applications of de moiver theorem1.png)
Sum of the Roots:
![699_Applications of de moiver theorem2.png](https://www.expertsmind.com/../CMSImages/699_Applications of de moiver theorem2.png)
Hence the sum of the roots of unity is zero.
Product of the Roots:
![1937_Applications of de moiver theorem3.png](https://www.expertsmind.com/../CMSImages/1937_Applications of de moiver theorem3.png)
If n is even ![1586_Applications of de moiver theorem4.png](https://www.expertsmind.com/../CMSImages/1586_Applications of de moiver theorem4.png)
If n is odd ![986_Applications of de moiver theorem5.png](https://www.expertsmind.com/../CMSImages/986_Applications of de moiver theorem5.png)
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.
|
![208_Applications of de moiver theorem6.png](https://www.expertsmind.com/CMSImages/208_Applications%20of%20de%20moiver%20theorem6.png)
|
Email based Applications of de moiver’s theorem Assignment Help -Homework Help
We at www.expertsmind.com offer email based Applications of de moiver’s theorem assignment help - homework help and projects assistance from k-12 school level to university and college level and engineering and management studies. We provide finest service of Mathematics assignment help and Mathematic homework help. Our experts are helping students in their studies and they offer instantaneous tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.
Expertsmind's best education services
- Quality assignment-homework help assistance 24x7 hrs
- Best qualified tutor's network
- Time on delivery
- Quality assurance before delivery
- 100% originality and fresh work