Mathematik

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(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>
+
|<math>\mathrm i</math>:=<math>\sqrt{-1} \qquad i^2 = -1</math>
-
|<math>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>
|}
|}
-
 
-
<math>z_1 + z_2 = (x_1 + x_2) + \mathrm i(y_1 + y_2)</math>
 
-
 
-
<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 + z_2 = </math>
+
|Produkt:
-
 
+
|<math>z_1 \cdot z_2 = </math>
-
<math>z_1 \cdot z_2 = </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

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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