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Lösung 3.2:4d

Aus Online Mathematik Brückenkurs 2

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K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel))
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For magnitudes of quotients, we have the arithmetical rule
For magnitudes of quotients, we have the arithmetical rule
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{{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,
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{{Displayed math||<math>\begin{align}
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{{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|}

Version vom 13:09, 10. Mär. 2009

For magnitudes of quotients, we have the arithmetical rule

zw=zw.

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

3+2i3−4i=3+2i3−4i=32+2232+(−4)2=9+49+16=1325=513. 
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.2:4d“