5,336
edits
Complex Numbers: Difference between revisions
→Basics
(→Basics) |
|||
| Line 12: | Line 12: | ||
* The angle is <math>\angle c = \arctan(b, a)</math>. | * The angle is <math>\angle c = \arctan(b, a)</math>. | ||
* The exponential representation is <math>c = |c| e^{i \theta}</math> where <math>\theta = \angle c</math>. | * The exponential representation is <math>c = |c| e^{i \theta}</math> where <math>\theta = \angle c</math>. | ||
** In this representation, <math>\theta</math> is known as the [[Wikipedia: argument | Argument]] and <code>|c|</code> is the modulus or absolute value. | |||
** Note that the word ''amplitude'' is overloaded and can refer to either the entire complex number, the absolute value, or the angle depending on context. | |||
* Addition and multiplication are as usual, but with <math>i^2 = -1</math>. | * Addition and multiplication are as usual, but with <math>i^2 = -1</math>. | ||