Mathematik

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m (komplexe Zahlen)
(komplexe Zahlen)
Line 42: Line 42:
|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>
 +
|}
 +
 +
'''<math>E(\varphi)</math>-Rechenregeln:'''
 +
{|
 +
|<math>E(\varphi+k\cdot2\phi) = E(\varphi)</math>
 +
|<math>|E(\varphi)| = 1</math>
 +
|-
 +
|<math>E(\varphi_1)\cdot E(\varphi_2) = E(\varphi_1 + \varphi_2)</math>
 +
|<math>E(\varphi)\cdot E(-\varphi) = 1</math>
 +
|-
 +
|<math>[E(\varphi)]^n = E(N\, \varphi)</math>
 +
|<math>E(\varphi) = e^{\mathrm i\,\phi}</math>
|}
|}

Revision as of 12:34, 17 September 2008

Analysis

MathImage


Geometrie

MathImage


komplexe Zahlen

Normalform

MathImage MathImage:=MathImage
MathImage MathImage
Summe MathImage
Produkt MathImage

Polarform:

MathImage MathImage
MathImage MathImage
Produkt: MathImage
Quotient: MathImage
Potenz: MathImage

MathImage-Rechenregeln:

MathImage MathImage
MathImage MathImage
MathImage MathImage

konjungierte komplexe Zahlen:

MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage
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