Complex Numbers: Difference between revisions
| Line 19: | Line 19: | ||
Euler's formula states: | Euler's formula states: | ||
<math display="block> | <math display="block"> | ||
e^{ix} = \cos(x) + i \sin(x) | e^{ix} = \cos(x) + i \sin(x) | ||
</math> | </math> | ||
| Line 25: | Line 25: | ||
===Properties=== | ===Properties=== | ||
* The conjugate is <math>e^{-ix}</math> since cosine is symmetric and sine is odd (i.e. <math>sin(-x) = -sin(x)</math>) | * The conjugate is <math>e^{-ix}</math> since cosine is symmetric and sine is odd (i.e. <math>sin(-x) = -sin(x)</math>) | ||
==Euler's Identity== | |||
Euler's Identity states: | |||
<math display="block"> | |||
e^{i \pi} + 1 = 0 | |||
</math> | |||
==Resources== | ==Resources== | ||
* [https://web.stanford.edu/~boyd/ee102/complex-primer.pdf https://web.stanford.edu/~boyd/ee102/complex-primer.pdf] Brief review of complex numbers | * [https://web.stanford.edu/~boyd/ee102/complex-primer.pdf https://web.stanford.edu/~boyd/ee102/complex-primer.pdf] Brief review of complex numbers | ||