Lösung 3.2:4d
Aus Online Mathematik Brückenkurs 2
(Unterschied zwischen Versionen)
K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)) |
K (Solution 3.2:4d moved to Lösung 3.2:4d: Robot: moved page) |
Version vom 10:38, 11. 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} |
