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Lösung 3.2:4c

Aus Online Mathematik Brückenkurs 2

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K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel))
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One way to determine the magnitude is to calculate the product <math>(3-4i)(3+2i)</math> and then to take the magnitude of the result, but for products we have that
One way to determine the magnitude is to calculate the product <math>(3-4i)(3+2i)</math> and then to take the magnitude of the result, but for products we have that
-
{{Displayed math||<math>|zw| = |z|\cdot |w|</math>}}
+
{{Abgesetzte Formel||<math>|zw| = |z|\cdot |w|</math>}}
and we can take the magnitude of the factors <math>3-4i</math> and <math>3+2i</math> and then multiply the magnitudes together,
and we can take the magnitude of the factors <math>3-4i</math> and <math>3+2i</math> and then multiply the magnitudes together,
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{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
|(3-4i)(3+2i)|
|(3-4i)(3+2i)|
&= |3-4i|\cdot |3+2i|\\[5pt]
&= |3-4i|\cdot |3+2i|\\[5pt]

Version vom 13:08, 10. Mär. 2009

One way to determine the magnitude is to calculate the product (3−4i)(3+2i) and then to take the magnitude of the result, but for products we have that

zw=zw

and we can take the magnitude of the factors 3−4i and 3+2i and then multiply the magnitudes together,

(3−4i)(3+2i)=3−4i3+2i=32+(−4)232+22=9+169+4=2513=513.
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.2:4c“