Lösung 3.2:1b - Versionsgeschichte

Martin um 18:36, 12. Mai 2009

2009-05-12T18:36:15Z

← Nächstältere Version		Version vom 18:36, 12. Mai 2009
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-	~~We can easily calculate~~ <math>z+u</math> ~~and~~ <math>z-u</math>,	+	Wir können einfach<math>z+u</math> und <math>z-u</math> berechnen,

	{{Abgesetzte Formel\|\|<math>\begin{align}		{{Abgesetzte Formel\|\|<math>\begin{align}
Zeile 6:		Zeile 6:
	\end{align}</math>}}		\end{align}</math>}}

-	~~and then mark them on the complex plane~~.	+	und in der komplexen Zahlenebene einzeichnen.

-	~~An alternative is to view~~ <math>z</math> ~~and~~ <math>u</math> ~~as vectors and~~ <math>z+u</math> ~~as a vector addition of~~ <math>z</math> ~~and~~ <math>u</math>.	+	Alternativ konnen wir <math>z</math> und <math>u</math> als Vektoren betrachten, und <math>z+u</math> wir die Addition von den Vektoren <math>z</math> und <math>u</math> sehen.

	[[Image:3_2_1_b1.gif\|center]]		[[Image:3_2_1_b1.gif\|center]]

-	~~We can either view the vector subtraction~~ <math>z-u</math> as <math>z+(-u)</math>,	+	Wir können entweder <math>z-u</math> als <math>z+(-u)</math> interpretieren,

	[[Image:3_2_1_b2.gif\|center]]		[[Image:3_2_1_b2.gif\|center]]

-	~~or interpret~~ <math>z-u</math> ~~from the vector relation~~	+	oder <math>z-u</math> von der Gleichung

	{{Abgesetzte Formel\|\|<math>z=(z-u)+u\,,</math>}}		{{Abgesetzte Formel\|\|<math>z=(z-u)+u\,,</math>}}

-	~~i.e.~~ <math>z-u</math> ~~is the vector we add to~~ <math>u</math> ~~to arrive at~~ <math>z</math>.	+	erhalten, wo also <math>z-u</math> der Vektor ist, den wir zu <math>u</math> addieren um <math>z</math> zu erhalten.

	[[Image:3_2_1_b3.gif\|center]]		[[Image:3_2_1_b3.gif\|center]]

Tekbot: Solution 3.2:1b moved to Lösung 3.2:1b: Robot: moved page

2009-03-11T10:34:35Z

Solution 3.2:1b moved to Lösung 3.2:1b: Robot: moved page

← Nächstältere Version

Version vom 10:34, 11. Mär. 2009

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

2009-03-10T13:07:34Z

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

← Nächstältere Version		Version vom 13:07, 10. Mär. 2009
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	We can easily calculate <math>z+u</math> and <math>z-u</math>,		We can easily calculate <math>z+u</math> and <math>z-u</math>,

-	{{~~Displayed math~~\|\|<math>\begin{align}	+	{{Abgesetzte Formel\|\|<math>\begin{align}
	z+u &= 2+i+(-1-2i) = 2-1+(1-2)i = 1-i,\\[5pt]		z+u &= 2+i+(-1-2i) = 2-1+(1-2)i = 1-i,\\[5pt]
	z-u &= 2+i-(-1-2i) = 2+1+(1+2)i = 3+3i,		z-u &= 2+i-(-1-2i) = 2+1+(1+2)i = 3+3i,
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	or interpret <math>z-u</math> from the vector relation		or interpret <math>z-u</math> from the vector relation

-	{{~~Displayed math~~\|\|<math>z=(z-u)+u\,,</math>}}	+	{{Abgesetzte Formel\|\|<math>z=(z-u)+u\,,</math>}}

	i.e. <math>z-u</math> is the vector we add to <math>u</math> to arrive at <math>z</math>.		i.e. <math>z-u</math> is the vector we add to <math>u</math> to arrive at <math>z</math>.

	[[Image:3_2_1_b3.gif\|center]]		[[Image:3_2_1_b3.gif\|center]]

Tek um 09:21, 29. Okt. 2008

2008-10-29T09:21:21Z

← Nächstältere Version		Version vom 09:21, 29. Okt. 2008
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-	{{NAVCONTENT_START}}
	We can easily calculate <math>z+u</math> and <math>z-u</math>,		We can easily calculate <math>z+u</math> and <math>z-u</math>,

-	<math>\begin{align}z+u&=2+i+(-1-2i)=2-1+(1-2)i=1-i,\\	+	{{Displayed math\|\|<math>\begin{align}
-	z-u&=2+i-(-1-2i)=2+1+(1+2)i=3+3i,\end{align}</math>	+	z+u &= 2+i+(-1-2i) = 2-1+(1-2)i = 1-i,\\[5pt]
		+	z-u &= 2+i-(-1-2i) = 2+1+(1+2)i = 3+3i,
		+	\end{align}</math>}}

	and then mark them on the complex plane.		and then mark them on the complex plane.
Zeile 15:		Zeile 16:
	[[Image:3_2_1_b2.gif\|center]]		[[Image:3_2_1_b2.gif\|center]]

-	or interpret <math>z-u</math> from the vector relation	+	or interpret <math>z-u</math> from the vector relation

-	<math>z=(z-u)+u</math>	+	{{Displayed math\|\|<math>z=(z-u)+u\,,</math>}}

	i.e. <math>z-u</math> is the vector we add to <math>u</math> to arrive at <math>z</math>.		i.e. <math>z-u</math> is the vector we add to <math>u</math> to arrive at <math>z</math>.

	[[Image:3_2_1_b3.gif\|center]]		[[Image:3_2_1_b3.gif\|center]]
-
-	{{NAVCONTENT_STOP}}

Jamesjmnewton um 10:30, 3. Okt. 2008

2008-10-03T10:30:46Z

← Nächstältere Version		Version vom 10:30, 3. Okt. 2008
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	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<~~center~~> ~~[[Image:3_2_1b-1(2).gif]]~~ </~~center~~>	+	We can easily calculate <math>z+u</math> and <math>z-u</math>,
-	~~{{NAVCONTENT_STOP}}~~	+
-	~~{{NAVCONTENT_START}}~~	+
-	<~~center~~> ~~[[Image:3_2_1b~~-~~2(2).gif]]~~ </~~center~~>	+
-	~~{{NAVCONTENT_STOP}}~~	+

		+	<math>\begin{align}z+u&=2+i+(-1-2i)=2-1+(1-2)i=1-i,\\
		+	z-u&=2+i-(-1-2i)=2+1+(1+2)i=3+3i,\end{align}</math>
		+
		+	and then mark them on the complex plane.
		+
		+	An alternative is to view <math>z</math> and <math>u</math> as vectors and <math>z+u</math> as a vector addition of <math>z</math> and <math>u</math>.

	[[Image:3_2_1_b1.gif\|center]]		[[Image:3_2_1_b1.gif\|center]]
		+
		+	We can either view the vector subtraction <math>z-u</math> as <math>z+(-u)</math>,

	[[Image:3_2_1_b2.gif\|center]]		[[Image:3_2_1_b2.gif\|center]]
		+
		+	or interpret <math>z-u</math> from the vector relation
		+
		+	<math>z=(z-u)+u</math>
		+
		+	i.e. <math>z-u</math> is the vector we add to <math>u</math> to arrive at <math>z</math>.

	[[Image:3_2_1_b3.gif\|center]]		[[Image:3_2_1_b3.gif\|center]]
		+
		+	{{NAVCONTENT_STOP}}

Tekbot: Lösning 3.2:1b moved to Solution 3.2:1b: Robot: moved page

2008-09-16T14:55:01Z

Lösning 3.2:1b moved to Solution 3.2:1b: Robot: moved page

← Nächstältere Version

Version vom 14:55, 16. Sep. 2008

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

2008-08-21T08:07:14Z

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

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-	[[~~Bild~~:3_2_1_b1.gif\|center]]	+	[[Image:3_2_1_b1.gif\|center]]

-	[[~~Bild~~:3_2_1_b2.gif\|center]]	+	[[Image:3_2_1_b2.gif\|center]]

-	[[~~Bild~~:3_2_1_b3.gif\|center]]	+	[[Image:3_2_1_b3.gif\|center]]

Madde um 13:47, 19. Aug. 2008

2008-08-19T13:47:09Z

← Nächstältere Version		Version vom 13:47, 19. Aug. 2008
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	[[Bild:3_2_1_b2.gif\|center]]		[[Bild:3_2_1_b2.gif\|center]]

-	[[Bild:~~3_2_1_b2~~.gif\|center]]	+	[[Bild:3_2_1_b3.gif\|center]]

Madde um 13:44, 19. Aug. 2008

2008-08-19T13:44:24Z

← Nächstältere Version		Version vom 13:44, 19. Aug. 2008
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		+	[[Bild:3_2_1_b1.gif\|center]]
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2008-04-07T12:02:08Z

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