De Moivre’s Theorem
What is De Moivre’s Theorem?
The De Moivre’s theorem is the basic theorem used in complex numbers for solving various problems. The De Moivre’s theorem states that,
(cos x + i sin x)n = cos(nx) + i sin(nx)
What are the uses of De Moivre’s Theorem?
The various uses of De Moivre’s theorem include the solving of complex roots, finding the power of the complex number and others.
Is De Moivre’s Theorem work for Non-Integer Powers?
No, De Moivre’s formula does not work for non-integer powers. The result for non-negative integers is the multiple-value different from the original results.
Who invented De Moivre’s Theorem?
The De Moivre’s theorem was first introduced by the French mathematician Abraham De Moivre.
DeMoivre’s Theorem
De Moivre’s theorem is one of the fundamental theorem of complex numbers which is used to solve various problems of complex numbers. This theorem is also widely used for solving trigonometric functions of multiple angles. DeMoivre’s Theorem is also called “De Moivre’s Identity” and “De Moivre’s Formula”. This theorem gets its name from the name of its founder the famous mathematician De Moivre.
In this article, we will learn about De Moivre’s Theorem, its proof, some examples based on the theorem, and others in detail.
Table of Content
- De Moivre’s Theorem Statement
- De Moivre’s Formula
- De Moivre’s Theorem Proof
- Uses of De Moivre’s Theorem
- Finding the Roots of Complex Numbers
- Power of Complex Numbers
- Solved Examples on De Moivre’s Theorem
- FAQs