De Moivre's theorem
Powers of a point on the unit circle rotate it n times as far. History: 1722.
How to work it out
- 1
The statement:
- 2
Powers of a point on the unit circle rotate it n times as far.
- 3
Below, the numbers in the table are computed by this site from the definition, not copied.
LaTeX source of the formulas on this page
\[ (\cos\theta + i\sin\theta)^n = \cos n\theta + i\sin n\theta \]
Powers of cos 30° + i sin 30° (computed)
| n | cos(30°n) | sin(30°n) |
|---|---|---|
| 1 | 0.8660 | 0.5000 |
| 2 | 0.5000 | 0.8660 |
| 3 | 0.0000 | 1.0000 |
| 4 | -0.5000 | 0.8660 |
| 6 | -1.0000 | 0.0000 |
| 12 | 1.0000 | -0.0000 |
Questions
What is the de moivre's theorem?
Powers of a point on the unit circle rotate it n times as far.
Who is the De Moivre's theorem associated with?
Leonhard Euler.