Lösung 3.2:4d - Versionsgeschichte

Martin um 12:38, 13. Mai 2009

Martin — Wed, 13 May 2009 12:38:32 GMT

← Nächstältere Version		Version vom 12:38, 13. Mai 2009
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-	~~For magnitudes of quotients~~, ~~we have the arithmetical rule~~	+	Für den Betrag von Brüchen, haben wir

	{{Abgesetzte Formel\|\|<math>\left\|\frac{z}{w}\right\| = \frac{\|z\|}{\|w\|}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\left\|\frac{z}{w}\right\| = \frac{\|z\|}{\|w\|}\,\textrm{.}</math>}}

-	~~We can therefore take the magnitude of the numerator and denominator separately and then divide the magnitudes by each other~~,	+	Also können wir den Betrag vom Zähler und Nenner je für sich berechnen, und dann durch einander dividieren,

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

Tekbot — Wed, 11 Mar 2009 10:38:55 GMT

← Nächstältere Version

Version vom 10:38, 11. Mär. 2009

Tekbot — Tue, 10 Mar 2009 13:09:04 GMT

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

← Nächstältere Version		Version vom 13:09, 10. Mär. 2009
Zeile 1:		Zeile 1:
	For magnitudes of quotients, we have the arithmetical rule		For magnitudes of quotients, we have the arithmetical rule

-	{{~~Displayed math~~\|\|<math>\left\|\frac{z}{w}\right\| = \frac{\|z\|}{\|w\|}\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>\left\|\frac{z}{w}\right\| = \frac{\|z\|}{\|w\|}\,\textrm{.}</math>}}

	We can therefore take the magnitude of the numerator and denominator separately and then divide the magnitudes by each other,		We can therefore take the magnitude of the numerator and denominator separately and then divide the magnitudes by each other,

-	{{~~Displayed math~~\|\|<math>\begin{align}	+	{{Abgesetzte Formel\|\|<math>\begin{align}
	\left\|\frac{3-4i}{3+2i}\right\|		\left\|\frac{3-4i}{3+2i}\right\|
	&= \frac{\|3-4i\|}{\|3+2i\|}		&= \frac{\|3-4i\|}{\|3+2i\|}

Tek — Wed, 29 Oct 2008 12:16:38 GMT

← Nächstältere Version		Version vom 12:16, 29. Okt. 2008
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	For magnitudes of quotients, we have the arithmetical rule		For magnitudes of quotients, we have the arithmetical rule

		+	{{Displayed math\|\|<math>\left\|\frac{z}{w}\right\| = \frac{\|z\|}{\|w\|}\,\textrm{.}</math>}}

-	~~<math>\left\| \frac{z}{w} \right\|=\frac{\left\| z \right\|}{\left\| w \right\|}</math>~~	+	We can therefore take the magnitude of the numerator and denominator separately and then divide the magnitudes by each other,

-		+	{{Displayed math\|\|<math>\begin{align}
-	~~We can therefore take the magnitude of the numerator and denominator separately and then divide the magnitudes by each other:~~	+	\left\|\frac{3-4i}{3+2i}\right\|
-		+	&= \frac{\|3-4i\|}{\|3+2i\|}
-		+	= \frac{\sqrt{3^2+(-4)^2}}{\sqrt{3^2+2^2}}
-	<math>\begin{align}	+	= \frac{\sqrt{9+16}}{\sqrt{9+4}}
-	& \left\| \frac{3-4i}{3+2i} \right\|=\frac{~~\left~~\| 3-4i ~~\right~~\|}{~~\left~~\| 3+2i ~~\right~~\|}=\frac{\sqrt{3^{2}+~~\left~~( -4 ~~\right~~)^{2}}}{\sqrt{3^{2}+2^{2}}}=\frac{\sqrt{9+16}}{\sqrt{9+4}} \\	+	= \frac{\sqrt{25}}{\sqrt{13}}
-	& =\frac{\sqrt{25}}{\sqrt{13}}=\frac{5}{\sqrt{13}} \\	+	= \frac{5}{\sqrt{13}}\,\textrm{.}
-	\end{align}</math>	+	\end{align}</math>}}

Ian — Wed, 22 Oct 2008 15:39:08 GMT

← Nächstältere Version		Version vom 15:39, 22. Okt. 2008
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-	{{~~NAVCONTENT_START~~}}	+	For magnitudes of quotients, we have the arithmetical rule
-	<~~center~~> ~~[[Image~~:~~3_2_4d.gif]]~~ <~~/center~~>	+
-	{{~~NAVCONTENT_STOP~~}}	+
		+	<math>\left\| \frac{z}{w} \right\|=\frac{\left\| z \right\|}{\left\| w \right\|}</math>
		+
		+
		+	We can therefore take the magnitude of the numerator and denominator separately and then divide the magnitudes by each other:
		+
		+
		+	<math>\begin{align}
		+	& \left\| \frac{3-4i}{3+2i} \right\|=\frac{\left\| 3-4i \right\|}{\left\| 3+2i \right\|}=\frac{\sqrt{3^{2}+\left( -4 \right)^{2}}}{\sqrt{3^{2}+2^{2}}}=\frac{\sqrt{9+16}}{\sqrt{9+4}} \\
		+	& =\frac{\sqrt{25}}{\sqrt{13}}=\frac{5}{\sqrt{13}} \\
		+	\end{align}</math>

Tekbot — Tue, 16 Sep 2008 14:59:21 GMT

← Nächstältere Version

Version vom 14:59, 16. Sep. 2008

Tekbot — Thu, 21 Aug 2008 08:09:24 GMT

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

Oskar — Mon, 07 Apr 2008 12:12:32 GMT

Ny sida: {{NAVCONTENT_START}} <center> Bild:3_2_4d.gif </center> {{NAVCONTENT_STOP}}

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