Mathematik

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m (komplexe Zahlen)
(komplexe Zahlen)
Line 31: Line 31:
{|
{|
|<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

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
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