Lösung 3.2:4a - Versionsgeschichte

Moni um 16:21, 22. Aug. 2009

2009-08-22T16:21:47Z

← Nächstältere Version		Version vom 16:21, 22. Aug. 2009
Zeile 1:		Zeile 1:
	Der Betrag von <math>3+4i</math> ist der Abstand zum Punkt <math>(0,0)</math> in der komplexen Zahlenebene.		Der Betrag von <math>3+4i</math> ist der Abstand zum Punkt <math>(0,0)</math> in der komplexen Zahlenebene.

-	Durch ~~das Gesetz~~ des Pythagoras erhalten wir den Abstand ~~wie~~	+	Durch den Satz des Pythagoras erhalten wir den Abstand

	{{Abgesetzte Formel\|\|<math>\|3+4i\| = \sqrt{3^2+4^2} = \sqrt{9+16} = \sqrt{25} = 5\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\|3+4i\| = \sqrt{3^2+4^2} = \sqrt{9+16} = \sqrt{25} = 5\,\textrm{.}</math>}}

2009-05-13T12:34:14Z

← Nächstältere Version		Version vom 12:34, 13. Mai 2009
Zeile 1:		Zeile 1:
-	~~The magnitude of the number~~ <math>3+4i</math> ~~is the number's distance to the origin~~ in ~~the complex number plane~~.	+	Der Betrag von <math>3+4i</math> ist der Abstand zum Punkt <math>(0,0)</math> in der komplexen Zahlenebene.

-	If we treat the line from the origin to <math>3+4i</math> as the hypotenuse in a right-angled triangle which has its legs parallel with the real and imaginary axes, then the Pythagorean theorem gives that the magnitude is	+	Durch das Gesetz des Pythagoras erhalten wir den Abstand wie

	{{Abgesetzte Formel\|\|<math>\|3+4i\| = \sqrt{3^2+4^2} = \sqrt{9+16} = \sqrt{25} = 5\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\|3+4i\| = \sqrt{3^2+4^2} = \sqrt{9+16} = \sqrt{25} = 5\,\textrm{.}</math>}}
Zeile 8:		Zeile 8:


-	~~Note~~: ~~In general, the magnitude of a complex number~~ <math>z=x+iy</math> ~~is equal to~~	+	Hinweis: Allgemein ist der Betrag einer komplexen Zahl <math>z=x+iy</math>,

	{{Abgesetzte Formel\|\|<math>\|z\| = \|x+iy\| = \sqrt{x^2+y^2}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\|z\| = \|x+iy\| = \sqrt{x^2+y^2}\,\textrm{.}</math>}}

2009-03-11T10:37:55Z

← Nächstältere Version

Version vom 10:37, 11. Mär. 2009

2009-03-10T13:08:34Z

Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)

← Nächstältere Version		Version vom 13:08, 10. Mär. 2009
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	If we treat the line from the origin to <math>3+4i</math> as the hypotenuse in a right-angled triangle which has its legs parallel with the real and imaginary axes, then the Pythagorean theorem gives that the magnitude is		If we treat the line from the origin to <math>3+4i</math> as the hypotenuse in a right-angled triangle which has its legs parallel with the real and imaginary axes, then the Pythagorean theorem gives that the magnitude is

-	{{~~Displayed math~~\|\|<math>\|3+4i\| = \sqrt{3^2+4^2} = \sqrt{9+16} = \sqrt{25} = 5\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>\|3+4i\| = \sqrt{3^2+4^2} = \sqrt{9+16} = \sqrt{25} = 5\,\textrm{.}</math>}}

	[[Image:3_2_4_a.gif\|center]]		[[Image:3_2_4_a.gif\|center]]
Zeile 10:		Zeile 10:
	Note: In general, the magnitude of a complex number <math>z=x+iy</math> is equal to		Note: In general, the magnitude of a complex number <math>z=x+iy</math> is equal to

-	{{~~Displayed math~~\|\|<math>\|z\| = \|x+iy\| = \sqrt{x^2+y^2}\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>\|z\| = \|x+iy\| = \sqrt{x^2+y^2}\,\textrm{.}</math>}}

2008-10-29T09:54:57Z

← Nächstältere Version		Version vom 09:54, 29. Okt. 2008
Zeile 1:		Zeile 1:
-	The magnitude of the number	+	The magnitude of the number <math>3+4i</math> is the number's distance to the origin in the complex number plane.
-	<math>~~\text{~~3}+~~\text{4}i~~</math>	+
-	is the number's distance to the origin in the complex number plane.	+

-	If we treat the line from the origin to	+	If we treat the line from the origin to <math>3+4i</math> as the hypotenuse in a right-angled triangle which has its legs parallel with the real and imaginary axes, then the Pythagorean theorem gives that the magnitude is
-	<math>~~\text{~~3}+~~\text{4}i~~</math>	+
-	as the hypotenuse in a right-angled triangle which has its ~~sides~~ parallel with the real and imaginary axes, then ~~Pythagoras'~~ theorem gives that the magnitude is	+
-		+
-		+
-	~~<math>\left\| \text{3}+\text{4}i \right\|=\sqrt{3^{2}+4^{2}}=\sqrt{9+16}=\sqrt{25}=5</math>~~	+

		+	{{Displayed math\|\|<math>\|3+4i\| = \sqrt{3^2+4^2} = \sqrt{9+16} = \sqrt{25} = 5\,\textrm{.}</math>}}

	[[Image:3_2_4_a.gif\|center]]		[[Image:3_2_4_a.gif\|center]]

-	NOTE: In general, the magnitude of a complex number
-	<math>z=x+iy</math>
-	is equal to

		+	Note: In general, the magnitude of a complex number <math>z=x+iy</math> is equal to

-	<math>~~\left~~\| z ~~\right~~\|=~~\left~~\| x+iy ~~\right~~\|=\sqrt{x^{2}+y^{2}}</math>	+	{{Displayed math\|\|<math>\|z\| = \|x+iy\| = \sqrt{x^2+y^2}\,\textrm{.}</math>}}

2008-10-22T15:19:15Z

← Nächstältere Version		Version vom 15:19, 22. Okt. 2008
Zeile 1:		Zeile 1:
-	{{~~NAVCONTENT_START~~}}	+	The magnitude of the number
-	<~~center~~> ~~[[Image:3_2_4a~~.~~gif]]~~ </~~center~~>	+	<math>\text{3}+\text{4}i</math>
-	{{~~NAVCONTENT_STOP~~}}	+	is the number's distance to the origin in the complex number plane.
		+
		+	If we treat the line from the origin to
		+	<math>\text{3}+\text{4}i</math>
		+	as the hypotenuse in a right-angled triangle which has its sides parallel with the real and imaginary axes, then Pythagoras' theorem gives that the magnitude is
		+
		+
		+	<math>\left\| \text{3}+\text{4}i \right\|=\sqrt{3^{2}+4^{2}}=\sqrt{9+16}=\sqrt{25}=5</math>
		+

	[[Image:3_2_4_a.gif\|center]]		[[Image:3_2_4_a.gif\|center]]
		+
		+	NOTE: In general, the magnitude of a complex number
		+	<math>z=x+iy</math>
		+	is equal to
		+
		+
		+	<math>\left\| z \right\|=\left\| x+iy \right\|=\sqrt{x^{2}+y^{2}}</math>

2008-09-16T14:58:21Z

← Nächstältere Version

Version vom 14:58, 16. Sep. 2008

2008-08-21T08:08:54Z

Robot: Automated text replacement (-[[Bild: +[[Image:)

2008-08-19T14:52:59Z

2008-04-07T12:10:42Z

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