Lösung 3.1:4a - Versionsgeschichte

Moni um 12:08, 22. Aug. 2009

Moni — Sat, 22 Aug 2009 12:08:05 GMT

← Nächstältere Version		Version vom 12:08, 22. Aug. 2009
Zeile 18:		Zeile 18:
	{{Abgesetzte Formel\|\|<math>2+3i=z\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>2+3i=z\,\textrm{.}</math>}}

-	Um zu kontrollieren ob wir richtig gerechnet haben, substituieren wir <math>z=2+3i</math>in der ursprünglichen Gleichung, und sehen dass	+	Um zu kontrollieren, ob wir richtig gerechnet haben, substituieren wir <math>z=2+3i</math>in der ursprünglichen Gleichung und sehen, dass

	{{Abgesetzte Formel\|\|<math>\begin{align}		{{Abgesetzte Formel\|\|<math>\begin{align}

Martin um 09:48, 12. Mai 2009

Martin — Tue, 12 May 2009 09:48:57 GMT

← Nächstältere Version		Version vom 09:48, 12. Mai 2009
Zeile 1:		Zeile 1:
-	~~A general strategy when solving equations is to try to get the unknown variable by itself on one side~~.	+	Um komplexe Gleichungen wie diese zu lösen, sammeln wir einfach alle Unbekannte Variablen auf einer Seite der Gleichung.

-	In ~~this case, we start by subtracting~~ <math>z</math> ~~from both sides~~,	+	In diesem Fall beginnen wir damit <math>z</math> von beiden Seiten zu subtrahieren,

	{{Abgesetzte Formel\|\|<math>z+3i-z=2z-2-z\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>z+3i-z=2z-2-z\,\textrm{.}</math>}}

-	~~Then we have a~~ <math>z</math> ~~left on the right-hand side~~,	+
		+	Jetzt haben wir nur ein <math>z</math> auf der rechten Seite,

	{{Abgesetzte Formel\|\|<math>3i=z-2\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>3i=z-2\,\textrm{.}</math>}}

-	~~We add~~ <math>2</math> ~~to both sides to remove the~~ <math>-2</math> ~~from the right hand side~~,	+	Wir addieren <math>2</math> zu beiden Seiten, um <math>-2</math> auf der rechten Seite loszuwerden,

	{{Abgesetzte Formel\|\|<math>3i+2=z-2+2\,,</math>}}		{{Abgesetzte Formel\|\|<math>3i+2=z-2+2\,,</math>}}

-	~~and after that we can just read off the solution~~,	+	Jetzt haben wir unsere Lösung,

	{{Abgesetzte Formel\|\|<math>2+3i=z\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>2+3i=z\,\textrm{.}</math>}}

-	~~To check that we have calculated correctly~~, ~~we substitute~~ <math>z=2+3i</math> ~~into the original equation and see that it is satisfied~~,	+	Um zu kontrollieren ob wir richtig gerechnet haben, substituieren wir <math>z=2+3i</math>in der ursprünglichen Gleichung, und sehen dass

	{{Abgesetzte Formel\|\|<math>\begin{align}		{{Abgesetzte Formel\|\|<math>\begin{align}
-	\text{~~LHS~~} &= z +3i = 2+3i+3i=2+6i\,,\\[5pt]	+	\text{Linke Seite} &= z +3i = 2+3i+3i=2+6i\,,\\[5pt]
-	\text{~~RHS~~} &= 2z-2 = 2(2+3i)-2 = 4 + 6i -2 = 2+6i\,\textrm{.}	+	\text{Rechte Seite} &= 2z-2 = 2(2+3i)-2 = 4 + 6i -2 = 2+6i\,\textrm{.}
	\end{align}</math>}}		\end{align}</math>}}

Tekbot: Solution 3.1:4a moved to Lösung 3.1:4a: Robot: moved page

Tekbot — Wed, 11 Mar 2009 10:32:15 GMT

Solution 3.1:4a moved to Lösung 3.1:4a: Robot: moved page

← Nächstältere Version

Version vom 10:32, 11. Mär. 2009

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

Tekbot — Tue, 10 Mar 2009 13:06:34 GMT

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

← Nächstältere Version		Version vom 13:06, 10. Mär. 2009
Zeile 3:		Zeile 3:
	In this case, we start by subtracting <math>z</math> from both sides,		In this case, we start by subtracting <math>z</math> from both sides,

-	{{~~Displayed math~~\|\|<math>z+3i-z=2z-2-z\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>z+3i-z=2z-2-z\,\textrm{.}</math>}}

	Then we have a <math>z</math> left on the right-hand side,		Then we have a <math>z</math> left on the right-hand side,

-	{{~~Displayed math~~\|\|<math>3i=z-2\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>3i=z-2\,\textrm{.}</math>}}

	We add <math>2</math> to both sides to remove the <math>-2</math> from the right hand side,		We add <math>2</math> to both sides to remove the <math>-2</math> from the right hand side,

-	{{~~Displayed math~~\|\|<math>3i+2=z-2+2\,,</math>}}	+	{{Abgesetzte Formel\|\|<math>3i+2=z-2+2\,,</math>}}

	and after that we can just read off the solution,		and after that we can just read off the solution,

-	{{~~Displayed math~~\|\|<math>2+3i=z\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>2+3i=z\,\textrm{.}</math>}}

	To check that we have calculated correctly, we substitute <math>z=2+3i</math> into the original equation and see that it is satisfied,		To check that we have calculated correctly, we substitute <math>z=2+3i</math> into the original equation and see that it is satisfied,

-	{{~~Displayed math~~\|\|<math>\begin{align}	+	{{Abgesetzte Formel\|\|<math>\begin{align}
	\text{LHS} &= z +3i = 2+3i+3i=2+6i\,,\\[5pt]		\text{LHS} &= z +3i = 2+3i+3i=2+6i\,,\\[5pt]
	\text{RHS} &= 2z-2 = 2(2+3i)-2 = 4 + 6i -2 = 2+6i\,\textrm{.}		\text{RHS} &= 2z-2 = 2(2+3i)-2 = 4 + 6i -2 = 2+6i\,\textrm{.}
	\end{align}</math>}}		\end{align}</math>}}

Tek um 07:15, 30. Okt. 2008

Tek — Thu, 30 Oct 2008 07:15:59 GMT

← Nächstältere Version		Version vom 07:15, 30. Okt. 2008
Zeile 1:		Zeile 1:
-	{{NAVCONTENT_START}}
	A general strategy when solving equations is to try to get the unknown variable by itself on one side.		A general strategy when solving equations is to try to get the unknown variable by itself on one side.

-	In this case, we start by subtracting z from both sides,	+	In this case, we start by subtracting <math>z</math> from both sides,

		+	{{Displayed math\|\|<math>z+3i-z=2z-2-z\,\textrm{.}</math>}}

-	<math>z~~+3i-z=2z-2-z.~~</math>	+	Then we have a <math>z</math> left on the right-hand side,

		+	{{Displayed math\|\|<math>3i=z-2\,\textrm{.}</math>}}

-	~~Then we have a z left on~~ the ~~right~~-hand side,	+	We add <math>2</math> to both sides to remove the <math>-2</math> from the right hand side,

		+	{{Displayed math\|\|<math>3i+2=z-2+2\,,</math>}}

-	~~<math>3i=z-2</math>.~~	+	and after that we can just read off the solution,

		+	{{Displayed math\|\|<math>2+3i=z\,\textrm{.}</math>}}

-	~~We add~~ <math>2</math> ~~to both sides to remove~~ the ~~<math>-2</math> from the right hand side~~	+	To check that we have calculated correctly, we substitute <math>z=2+3i</math> into the original equation and see that it is satisfied,

-		+	{{Displayed math\|\|<math>\begin{align}
-	<math~~>3i+2=z-2+2</math>~~	+	\text{LHS} &= z +3i = 2+3i+3i=2+6i\,,\\[5pt]
-		+	\text{RHS} &= 2z-2 = 2(2+3i)-2 = 4 + 6i -2 = 2+6i\,\textrm{.}
-		+	\end{align}</math>}}
-	~~and after that we can just read off the solution:~~	+
-		+
-		+
-	~~<math>2+3i=z</math>~~	+
-		+
-		+
-	~~To check that we have calculated correctly, we substitute z=2+3i into the original equation and see that it is satisfied:~~	+
-		+
-		+
-	<math>\begin{align}LHS &= z +3i = 2+3i+3i=2+6i,\\	+
-	RHS &= 2z-2 = 2(2+3i)-2 = 4 + 6i -2 = 2+6i.\end{align}</math>	+
-		+
-		+
-	~~{{NAVCONTENT_STOP~~}}	+

Jamesjmnewton um 10:37, 23. Sep. 2008

Jamesjmnewton — Tue, 23 Sep 2008 10:37:57 GMT

← Nächstältere Version		Version vom 10:37, 23. Sep. 2008
Zeile 1:		Zeile 1:
	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<~~center~~> ~~[[Image~~:~~3_1_4a~~.~~gif]]~~ </~~center~~>	+	A general strategy when solving equations is to try to get the unknown variable by itself on one side.
		+
		+	In this case, we start by subtracting z from both sides,
		+
		+
		+	<math>z+3i-z=2z-2-z.</math>
		+
		+
		+	Then we have a z left on the right-hand side,
		+
		+
		+	<math>3i=z-2</math>.
		+
		+
		+	We add <math>2</math> to both sides to remove the <math>-2</math> from the right hand side
		+
		+
		+	<math>3i+2=z-2+2</math>
		+
		+
		+	and after that we can just read off the solution:
		+
		+
		+	<math>2+3i=z</math>
		+
		+
		+	To check that we have calculated correctly, we substitute z=2+3i into the original equation and see that it is satisfied:
		+
		+
		+	<math>\begin{align}LHS &= z +3i = 2+3i+3i=2+6i,\\
		+	RHS &= 2z-2 = 2(2+3i)-2 = 4 + 6i -2 = 2+6i.\end{align}</math>
		+
		+
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}

Tekbot: Lösning 3.1:4a moved to Solution 3.1:4a: Robot: moved page

Tekbot — Tue, 16 Sep 2008 14:52:41 GMT

Lösning 3.1:4a moved to Solution 3.1:4a: Robot: moved page

← Nächstältere Version

Version vom 14:52, 16. Sep. 2008

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

Tekbot — Thu, 21 Aug 2008 08:06:04 GMT

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

← Nächstältere Version		Version vom 08:06, 21. Aug. 2008
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	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<center> [[~~Bild~~:3_1_4a.gif]] </center>	+	<center> [[Image:3_1_4a.gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}

Oskar: Ny sida: {{NAVCONTENT_START}} Bild:3_1_4a.gif {{NAVCONTENT_STOP}}

Oskar — Mon, 07 Apr 2008 10:51:59 GMT

Ny sida: {{NAVCONTENT_START}} <center> Bild:3_1_4a.gif </center> {{NAVCONTENT_STOP}}

Neue Seite

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<center> [[Bild:3_1_4a.gif]] </center>
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