Difference between revisions of "DeMoivere’s Theorem"
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| − | * [https://mathresearch.utsa.edu/wikiFiles/MAT1093/DeMoivere%E2%80%99s%20Theorem/Esparza%201093%20Notes%20Week%2012.pdf | + | De Moivre's Theorem states that for a complex number <math> z = r(\cos{\theta} + i\sin{\theta}) </math> and integer <math> n </math>, then |
| − | * [https://www.youtube.com/watch?v=hTKXSIT_MpU Application of | + | |
| + | <math> [r(\cos{\theta} + i\sin{\theta})]^n = r^n(\cos{(n\theta)} + i\sin{(n\theta}))</math>. | ||
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| + | ==Resources== | ||
| + | * [https://mathresearch.utsa.edu/wikiFiles/MAT1093/DeMoivere%E2%80%99s%20Theorem/Esparza%201093%20Notes%20Week%2012.pdf De Moivre’s Theorem]. Written notes created by Professor Esparza, UTSA. | ||
| + | * [https://www.youtube.com/watch?v=hTKXSIT_MpU Application of DeMoivre's Theorem]. Produced by Professor Zachary Sharon, UTSA. | ||
| + | * [https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/05%3A_Complex_Numbers_and_Polar_Coordinates/5.03%3A_DeMoivres_Theorem_and_Powers_of_Complex_Numbers De Moivre's Theorem and Powers of Complex Numbers], Mathematics LibreTexts | ||
Revision as of 20:09, 23 September 2021
De Moivre's Theorem states that for a complex number and integer , then
.
![{\displaystyle [r(\cos {\theta }+i\sin {\theta })]^{n}=r^{n}(\cos {(n\theta )}+i\sin {(n\theta }))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/229e67d289431facbad91c256e076f702d03ffb0)
Resources
- De Moivre’s Theorem. Written notes created by Professor Esparza, UTSA.
- Application of DeMoivre's Theorem. Produced by Professor Zachary Sharon, UTSA.
- De Moivre's Theorem and Powers of Complex Numbers, Mathematics LibreTexts
