de Moivre identity
From the Euler relation
it follows that
where . This is called de Moivre’s formula, and besides being generally useful, it’s a convenient way to remember double- (and higher-multiple-) angle formulas. For example,
Since the imaginary parts and real parts on each side must be equal, we must have
and
Title | de Moivre identity |
Canonical name | DeMoivreIdentity |
Date of creation | 2013-03-22 12:20:45 |
Last modified on | 2013-03-22 12:20:45 |
Owner | Daume (40) |
Last modified by | Daume (40) |
Numerical id | 11 |
Author | Daume (40) |
Entry type | Theorem |
Classification | msc 12E10 |
Synonym | de Moivre’s theorem |
Synonym | de Moivre’s formula |
Related topic | EulerRelation |
Related topic | DoubleAngleIdentity |
Related topic | ArgumentOfProductAndSum |
Related topic | ArgumentOfProductAndQuotient |