Mathematik
From SkyWiki
(Difference between revisions)
(→komplexe Zahlen) |
(→komplexe Zahlen) |
||
| Line 15: | Line 15: | ||
{| | {| | ||
|<math>z = x\, +\, \mathrm i y \quad</math> | |<math>z = x\, +\, \mathrm i y \quad</math> | ||
| - | |<math>\mathrm i</math>:=<math>\sqrt{-1} | + | |<math>\mathrm i</math>:=<math>\sqrt{-1} \qquad i^2 = -1</math> |
| - | + | ||
|- | |- | ||
|<math>x = \operatorname{Re}\, z</math> | |<math>x = \operatorname{Re}\, z</math> | ||
|<math>y = \operatorname{Im}\, z</math> | |<math>y = \operatorname{Im}\, z</math> | ||
| + | |- | ||
| + | |Summe | ||
| + | |<math>z_1 + z_2 = (x_1 + x_2) + \mathrm i(y_1 + y_2)</math> | ||
| + | |- | ||
| + | |Produkt | ||
| + | |<math>z_1 \cdot z_2 = (x_1x_2-y_1y_2) + \mathrm i(x_1y_2 + x_2_y_1)</math> | ||
|} | |} | ||
| - | |||
| - | |||
| - | |||
| - | |||
| - | |||
Polarform: | Polarform: | ||
{| | {| | ||
| - | |<math>z = |z| \cdot E(\varphi) = |z| \cdot(cos\varphi + \mathrm i\sin\varphi)</math> | + | |<math>z = |z| \cdot E(\varphi)</math> |
| + | |<math>E(\varphi) = |z| \cdot(cos\varphi + \mathrm i\,\sin\varphi)</math> | ||
| + | |- | ||
|<math>\varphi = arc(z)</math> | |<math>\varphi = arc(z)</math> | ||
|<math>\tan\varphi = \frac y x</math> | |<math>\tan\varphi = \frac y x</math> | ||
| - | + | |- | |
| - | <math>z_1 | + | |Produkt: |
| - | + | |<math>z_1 \cdot z_2 = </math> | |
| - | <math> | + | |- |
| + | |Quotient: | ||
| + | |<math>\frac{z_1 }{z_2} = </math> | ||
| + | |- | ||
| + | |Potenz: | ||
| + | |<math>{z}^n = </math> | ||
| + | |} | ||
[[category:Mathematik]] | [[category:Mathematik]] | ||
[[category:remember]] | [[category:remember]] | ||
Revision as of 12:11, 17 September 2008
Analysis
Geometrie
komplexe Zahlen
Normalform:
| Summe | |
| Produkt |
Polarform:
| Produkt: | |
| Quotient: | |
| Potenz: |
