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Lösung 3.2:6d

Aus Online Mathematik Brückenkurs 2

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K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel))
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We can determine the number's magnitude directly using the distance formula,
We can determine the number's magnitude directly using the distance formula,
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{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
\bigl|\sqrt{10}+\sqrt{30}i\bigr|
\bigl|\sqrt{10}+\sqrt{30}i\bigr|
&= \sqrt{\bigl(\sqrt{10}\,\bigr)^2+\bigl(\sqrt{30}\,\bigr)^2}\\[5pt]
&= \sqrt{\bigl(\sqrt{10}\,\bigr)^2+\bigl(\sqrt{30}\,\bigr)^2}\\[5pt]
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The polar form is
The polar form is
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{{Displayed math||<math>2\sqrt{10}\Bigl( \cos\frac{\pi}{3} + i\sin\frac{\pi}{3} \Bigr)\,\textrm{.}</math>}}
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{{Abgesetzte Formel||<math>2\sqrt{10}\Bigl( \cos\frac{\pi}{3} + i\sin\frac{\pi}{3} \Bigr)\,\textrm{.}</math>}}

Version vom 13:10, 10. Mär. 2009

We can determine the number's magnitude directly using the distance formula,

10+30i=102+302=10+30=40=410=210.

In addition, the number lies in the first quadrant and we can therefore determine the argument using simple trigonometry.

Image:3_2_6_d_bild.gif Image:3_2_6_d_bildtext.gif

The polar form is

210cos3+isin3. 
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.2:6d“