Lösung 3.1:3 - Versionsgeschichte

Martin um 09:11, 12. Mai 2009

Martin — Tue, 12 May 2009 09:11:37 GMT

← Nächstältere Version		Version vom 09:11, 12. Mai 2009
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-	~~In order to be able to see the expression's real and imaginary parts directly~~, ~~we treat it as an ordinary quotient of two complex numbers and multiply top and bottom by the complex conjugate of the denominator~~,	+	Wir müssen den Ausdruck in Real- und Imaginärteil aufteilen, um zu sehen wann der Ausdruck rein imaginär ist. Wir erweitern dazu den Bruch mit den konjugiert komplexen Nenner,

	{{Abgesetzte Formel\|\|<math>\begin{align}		{{Abgesetzte Formel\|\|<math>\begin{align}
Zeile 9:		Zeile 9:
	\end{align}</math>}}		\end{align}</math>}}

-	The expression has real part equal to zero when <math>6+a=0</math>, i.e. <math>a=-6</math>.

		+	Der Realteil des Ausdruckes ist null wenn <math>6+a=0</math>, also wenn <math>a=-6</math>.

-	~~Note~~: ~~Think about how to solve the problem if~~ <math>a</math> ~~is not a real number.~~	+
		+	Hinweis: Wie würden wir das Problem lösen, wenn <math>a</math> nicht reell ist?

Tekbot — Wed, 11 Mar 2009 10:31:55 GMT

Solution 3.1:3 moved to Lösung 3.1:3: Robot: moved page

← Nächstältere Version

Version vom 10:31, 11. Mär. 2009

Tekbot — Tue, 10 Mar 2009 13:06:24 GMT

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

← Nächstältere Version		Version vom 13:06, 10. Mär. 2009
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	In order to be able to see the expression's real and imaginary parts directly, we treat it as an ordinary quotient of two complex numbers and multiply top and bottom by the complex conjugate of the denominator,		In order to be able to see the expression's real and imaginary parts directly, we treat it as an ordinary quotient of two complex numbers and multiply top and bottom by the complex conjugate of the denominator,

-	{{~~Displayed math~~\|\|<math>\begin{align}	+	{{Abgesetzte Formel\|\|<math>\begin{align}
	\frac{3+i}{2+ai}		\frac{3+i}{2+ai}
	&= \frac{(3+i)(2-ai)}{(2+ai)(2-ai)}\\[5pt]		&= \frac{(3+i)(2-ai)}{(2+ai)(2-ai)}\\[5pt]

Tek — Thu, 30 Oct 2008 07:11:13 GMT

← Nächstältere Version		Version vom 07:11, 30. Okt. 2008
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-	~~{{NAVCONTENT_START}}~~	+	In order to be able to see the expression's real and imaginary parts directly, we treat it as an ordinary quotient of two complex numbers and multiply top and bottom by the complex conjugate of the denominator,
-	In order to be able to see the expression's real and imaginary parts directly, we treat it as an ordinary quotient of two complex numbers and multiply top and bottom by the complex conjugate of the ~~numerator:~~	+
-		+
-		+
-	~~<math>\begin{align}\frac{3+i}{2+ai}&=\frac{(3+i)(2-ai)}{(2+ai)(2-ai)}\\~~	+
-	~~&=\frac{3\cdot 2-3\cdot ai +i\cdot 2-ai^2}{2^2-(ai)^2}\\~~	+
-	~~&=\frac{6+a+(2-3a)i}{4+a^2}\\~~	+
-	~~&=\frac{6+a}{4+a^2}+\frac{2-3a}{4+a^2}i.\end{align}</math>~~	+

		+	{{Displayed math\|\|<math>\begin{align}
		+	\frac{3+i}{2+ai}
		+	&= \frac{(3+i)(2-ai)}{(2+ai)(2-ai)}\\[5pt]
		+	&= \frac{3\cdot 2-3\cdot ai +i\cdot 2-ai^2}{2^2-(ai)^2}\\[5pt]
		+	&= \frac{6+a+(2-3a)i}{4+a^2}\\[5pt]
		+	&= \frac{6+a}{4+a^2}+\frac{2-3a}{4+a^2}\,i\,\textrm{.}
		+	\end{align}</math>}}

	The expression has real part equal to zero when <math>6+a=0</math>, i.e. <math>a=-6</math>.		The expression has real part equal to zero when <math>6+a=0</math>, i.e. <math>a=-6</math>.

-	NOTE: Think about how to solve the problem if a is not a real number.

-	~~{{NAVCONTENT_STOP}}~~	+	Note: Think about how to solve the problem if <math>a</math> is not a real number.

Lina — Thu, 25 Sep 2008 16:13:01 GMT

← Nächstältere Version		Version vom 16:13, 25. Sep. 2008
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	The expression has real part equal to zero when <math>6+a=0</math>, i.e. <math>a=-6</math>.		The expression has real part equal to zero when <math>6+a=0</math>, i.e. <math>a=-6</math>.

-	NOTE: Think about how to solve the problem is a is not a real number.	+	NOTE: Think about how to solve the problem if a is not a real number.

	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}

Jamesjmnewton — Tue, 23 Sep 2008 10:29:46 GMT

← Nächstältere Version		Version vom 10:29, 23. Sep. 2008
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	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<~~center~~> ~~[[Image:3_1_3~~.~~gif]]~~ </~~center~~>	+	In order to be able to see the expression's real and imaginary parts directly, we treat it as an ordinary quotient of two complex numbers and multiply top and bottom by the complex conjugate of the numerator:
		+
		+
		+	<math>\begin{align}\frac{3+i}{2+ai}&=\frac{(3+i)(2-ai)}{(2+ai)(2-ai)}\\
		+	&=\frac{3\cdot 2-3\cdot ai +i\cdot 2-ai^2}{2^2-(ai)^2}\\
		+	&=\frac{6+a+(2-3a)i}{4+a^2}\\
		+	&=\frac{6+a}{4+a^2}+\frac{2-3a}{4+a^2}i.\end{align}</math>
		+
		+
		+	The expression has real part equal to zero when <math>6+a=0</math>, i.e. <math>a=-6</math>.
		+
		+	NOTE: Think about how to solve the problem is a is not a real number.
		+
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}

Tekbot — Tue, 16 Sep 2008 14:52:21 GMT

Lösning 3.1:3 moved to Solution 3.1:3: Robot: moved page

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Version vom 14:52, 16. Sep. 2008

Tekbot — Thu, 21 Aug 2008 08:05:54 GMT

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

Oskar — Mon, 07 Apr 2008 10:51:10 GMT

Ny sida: {{NAVCONTENT_START}} <center> Bild:3_1_3.gif </center> {{NAVCONTENT_STOP}}

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