| Line 1: | Line 1: | ||
Euler's identity | Euler's identity | ||
| − | <math> e^{ | + | <math> e^{j \pi} + 1 = 0, \,\! </math> |
Euler's formula | Euler's formula | ||
| − | <math> e^{ | + | <math> e^{jx} = \cos x + i \sin x \,\! </math> |
| − | <math> | + | <math> \cos x = \mathrm{Re}\{e^{ix}\} ={e^{ix} + e^{-ix} \over 2}</math> |
| + | |||
| + | <math> \sin x = \mathrm{Im}\{e^{ix}\} ={e^{ix} - e^{-ix} \over 2i}. </math> | ||
| + | |||
| + | <math> \cos(y) = {e^{-jy} + e^{jy} \over 2}</math> | ||
Revision as of 19:38, 22 July 2009
Euler's identity
$ e^{j \pi} + 1 = 0, \,\! $
Euler's formula
$ e^{jx} = \cos x + i \sin x \,\! $
$ \cos x = \mathrm{Re}\{e^{ix}\} ={e^{ix} + e^{-ix} \over 2} $
$ \sin x = \mathrm{Im}\{e^{ix}\} ={e^{ix} - e^{-ix} \over 2i}. $
$ \cos(y) = {e^{-jy} + e^{jy} \over 2} $
