Lösung 3.2:4d
Aus Online Mathematik Brückenkurs 2
(Unterschied zwischen Versionen)
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For magnitudes of quotients, we have the arithmetical rule | For magnitudes of quotients, we have the arithmetical rule | ||
- | {{ | + | {{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, | ||
- | {{ | + | {{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
\displaystyle \left|\frac{z}{w}\right| = \frac{|z|}{|w|}\,\textrm{.} |
We can therefore take the magnitude of the numerator and denominator separately and then divide the magnitudes by each other,
\displaystyle \begin{align}
\left|\frac{3-4i}{3+2i}\right| &= \frac{|3-4i|}{|3+2i|} = \frac{\sqrt{3^2+(-4)^2}}{\sqrt{3^2+2^2}} = \frac{\sqrt{9+16}}{\sqrt{9+4}} = \frac{\sqrt{25}}{\sqrt{13}} = \frac{5}{\sqrt{13}}\,\textrm{.} \end{align} |