Mathematik
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{| | {| | ||
|<math>z = |z| \cdot E(\varphi)</math> | |<math>z = |z| \cdot E(\varphi)</math> | ||
| - | |<math>E(\varphi) = |z| \cdot(cos\varphi + \mathrm i\,\sin\varphi)</math> | + | |<math>E(\varphi) = |z| \cdot(\cos\varphi + \mathrm i\,\sin\varphi)</math> |
|- | |- | ||
|<math>\varphi = arc(z)</math> | |<math>\varphi = arc(z)</math> | ||
| Line 37: | Line 37: | ||
|- | |- | ||
|Produkt: | |Produkt: | ||
| - | |<math>z_1 \cdot z_2 = </math> | + | |<math>z_1 \cdot z_2 = |z_1||z_2| \cdot E(\varphi_1+\varphi_2) = |z_1||z_2| (\cos(\varphi_1+\varphi2) + \mathrm i\, \sin(\varphi_1+\varphi_2))</math> |
|- | |- | ||
|Quotient: | |Quotient: | ||
| - | |<math>\frac{z_1 }{z_2} = </math> | + | |<math>\frac{z_1}{z_2} = \frac{|z_1|}{|z_2|} E(\varphi_1-\varphi_2) = \frac{|z_1|}{|z_2|} (\cos(\varphi_1-\varphi2) + \mathrm i\, \sin(\varphi_1-\varphi_2))</math> |
|- | |- | ||
|Potenz: | |Potenz: | ||
| - | |<math>{z}^n = |z|^n E(n\, \varphi) = |z|^n (cos\, n \varphi + \mathrm i\,\sin\, n \varphi)</math> | + | |<math>{z}^n = |z|^n E(n\, \varphi) = |z|^n (\cos\, n \varphi + \mathrm i\,\sin\, n \varphi)</math> |
|} | |} | ||
Revision as of 12:17, 17 September 2008
Analysis
Geometrie
komplexe Zahlen
Normalform:
| Summe | |
| Produkt |
Polarform:
| Produkt: | |
| Quotient: | |
| Potenz: |
