Lösung 3.3:1b - Versionsgeschichte

Sekretariat1 um 07:40, 1. Sep. 2009

Sekretariat1 — Tue, 01 Sep 2009 07:40:20 GMT

← Nächstältere Version		Version vom 07:40, 1. Sep. 2009
Zeile 1:		Zeile 1:
-	Zuerst bringen wir <math>\frac{1}{2}+i\frac{\sqrt{3}}{2}</math> ~~auf~~ Polarform.	+	Zuerst bringen wir <math>\frac{1}{2}+i\frac{\sqrt{3}}{2}</math> in Polarform.

	<center>[[Image:3_3_1_b.gif]] [[Image:3_3_1_b_text.gif]]</center>		<center>[[Image:3_3_1_b.gif]] [[Image:3_3_1_b_text.gif]]</center>

Martin — Mon, 18 May 2009 14:43:42 GMT

← Nächstältere Version		Version vom 14:43, 18. Mai 2009
Zeile 1:		Zeile 1:
-	~~First, we write the number~~ <math>\frac{1}{2}+i\frac{\sqrt{3}}{2}</math> ~~in polar form~~.	+	Zuerst bringen wir <math>\frac{1}{2}+i\frac{\sqrt{3}}{2}</math> auf Polarform.

	<center>[[Image:3_3_1_b.gif]] [[Image:3_3_1_b_text.gif]]</center>		<center>[[Image:3_3_1_b.gif]] [[Image:3_3_1_b_text.gif]]</center>

-	~~Thus,~~	+	Daher ist

	{{Abgesetzte Formel\|\|<math>\frac{1}{2}+i\frac{\sqrt{3}}{2} = 1\cdot \Bigl(\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}\Bigr)</math>}}		{{Abgesetzte Formel\|\|<math>\frac{1}{2}+i\frac{\sqrt{3}}{2} = 1\cdot \Bigl(\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}\Bigr)</math>}}

-	~~and de Moivre's formula gives~~	+	und durch den Moivreschen Satz erhalten wir

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

Tekbot — Wed, 11 Mar 2009 10:42:55 GMT

← Nächstältere Version

Version vom 10:42, 11. Mär. 2009

Tekbot — Tue, 10 Mar 2009 13:10:54 GMT

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

← Nächstältere Version		Version vom 13:10, 10. Mär. 2009
Zeile 5:		Zeile 5:
	Thus,		Thus,

-	{{~~Displayed math~~\|\|<math>\frac{1}{2}+i\frac{\sqrt{3}}{2} = 1\cdot \Bigl(\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}\Bigr)</math>}}	+	{{Abgesetzte Formel\|\|<math>\frac{1}{2}+i\frac{\sqrt{3}}{2} = 1\cdot \Bigl(\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}\Bigr)</math>}}

	and de Moivre's formula gives		and de Moivre's formula gives

-	{{~~Displayed math~~\|\|<math>\begin{align}	+	{{Abgesetzte Formel\|\|<math>\begin{align}
	\Bigl(\frac{1}{2}+i\frac{\sqrt{3}}{2}\Bigr)^{12}		\Bigl(\frac{1}{2}+i\frac{\sqrt{3}}{2}\Bigr)^{12}
	&= 1^{12}\cdot\Bigl(\cos\Bigl(12\cdot\frac{\pi}{3}\Bigr) + i\sin\Bigl(12\cdot\frac{\pi}{3}\Bigr)\Bigr)\\[5pt]		&= 1^{12}\cdot\Bigl(\cos\Bigl(12\cdot\frac{\pi}{3}\Bigr) + i\sin\Bigl(12\cdot\frac{\pi}{3}\Bigr)\Bigr)\\[5pt]

Tek — Thu, 30 Oct 2008 08:55:36 GMT

← Nächstältere Version		Version vom 08:55, 30. Okt. 2008
Zeile 1:		Zeile 1:
-	First, we write the number	+	First, we write the number <math>\frac{1}{2}+i\frac{\sqrt{3}}{2}</math> in polar form.
-	<math>\frac{1}{2}+i\frac{\sqrt{3}}{2}</math>	+
-	in polar form.	+

-		+	<center>[[Image:3_3_1_b.gif]] [[Image:3_3_1_b_text.gif]]</center>
-	[[Image:3_3_1_b.gif]] [[Image:3_3_1_b_text.gif]]	+

	Thus,		Thus,

-		+	{{Displayed math\|\|<math>\frac{1}{2}+i\frac{\sqrt{3}}{2} = 1\cdot \Bigl(\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}\Bigr)</math>}}
-	<math>\frac{1}{2}+i\frac{\sqrt{3}}{2}=1\~~centerdot~~ \~~left~~( \cos \frac{\pi }{3}+i\sin \frac{\pi }{3} \~~right~~)</math>	+
-		+

	and de Moivre's formula gives		and de Moivre's formula gives

-		+	{{Displayed math\|\|<math>\begin{align}
-	<math>\begin{align}	+	\Bigl(\frac{1}{2}+i\frac{\sqrt{3}}{2}\Bigr)^{12}
-	& \~~left~~( \frac{1}{2}+i\frac{\sqrt{3}}{2} \~~right~~)^{12}=1^{12}\~~centerdot~~ \~~left~~( \cos 12\~~centerdot~~ \frac{\pi }{3}+i\sin 12\~~centerdot~~ \frac{\pi }{3} \~~right~~) \\	+	&= 1^{12}\cdot\Bigl(\cos\Bigl(12\cdot\frac{\pi}{3}\Bigr) + i\sin\Bigl(12\cdot\frac{\pi}{3}\Bigr)\Bigr)\\[5pt]
-	& =1\~~centerdot \left~~( \cos 4\pi +i\sin 4\pi ~~\right~~) \\	+	&= 1\cdot (\cos 4\pi + i\sin 4\pi)\\[5pt]
-	& =1\~~centerdot \left~~( 1+i\~~centerdot~~ 0 ~~\right~~)=1 \\	+	&= 1\cdot (1+i\cdot 0)\\[5pt]
-	\end{align}</math>	+	&= 1\,\textrm{.}
		+	\end{align}</math>}}

Ian — Fri, 24 Oct 2008 07:14:44 GMT

← Nächstältere Version		Version vom 07:14, 24. Okt. 2008
Zeile 1:		Zeile 1:
-	{{~~NAVCONTENT_START~~}}	+	First, we write the number
-	~~<center> [[Image:3_3_1b.gif]]~~ </~~center~~>	+	<math>\frac{1}{2}+i\frac{\sqrt{3}}{2}</math>
-	~~{{NAVCONTENT_STOP}}~~	+	in polar form.
		+

	[[Image:3_3_1_b.gif]] [[Image:3_3_1_b_text.gif]]		[[Image:3_3_1_b.gif]] [[Image:3_3_1_b_text.gif]]
		+
		+	Thus,
		+
		+
		+	<math>\frac{1}{2}+i\frac{\sqrt{3}}{2}=1\centerdot \left( \cos \frac{\pi }{3}+i\sin \frac{\pi }{3} \right)</math>
		+
		+
		+	and de Moivre's formula gives
		+
		+
		+	<math>\begin{align}
		+	& \left( \frac{1}{2}+i\frac{\sqrt{3}}{2} \right)^{12}=1^{12}\centerdot \left( \cos 12\centerdot \frac{\pi }{3}+i\sin 12\centerdot \frac{\pi }{3} \right) \\
		+	& =1\centerdot \left( \cos 4\pi +i\sin 4\pi \right) \\
		+	& =1\centerdot \left( 1+i\centerdot 0 \right)=1 \\
		+	\end{align}</math>

Tekbot — Tue, 16 Sep 2008 15:03:21 GMT

← Nächstältere Version

Version vom 15:03, 16. Sep. 2008

Madde — Thu, 21 Aug 2008 12:41:35 GMT

Tekbot — Thu, 21 Aug 2008 08:11:24 GMT

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

Oskar — Mon, 07 Apr 2008 13:29:56 GMT

Ny sida: {{NAVCONTENT_START}} <center> Bild:3_3_1b.gif </center> {{NAVCONTENT_STOP}}

Neue Seite

{{NAVCONTENT_START}}
<center> [[Bild:3_3_1b.gif]] </center>
{{NAVCONTENT_STOP}}