Lösung 3.2:4c
Aus Online Mathematik Brückenkurs 2
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Version vom 10:38, 11. Mär. 2009
One way to determine the magnitude is to calculate the product \displaystyle (3-4i)(3+2i) and then to take the magnitude of the result, but for products we have that
| \displaystyle |zw| = |z|\cdot |w| |
and we can take the magnitude of the factors \displaystyle 3-4i and \displaystyle 3+2i and then multiply the magnitudes together,
| \displaystyle \begin{align}
|(3-4i)(3+2i)| &= |3-4i|\cdot |3+2i|\\[5pt] &= \sqrt{3^2+(-4)^2}\cdot\sqrt{3^2+2^2}\\[5pt] &= \sqrt{9+16}\sqrt{9+4}\\[5pt] &= \sqrt{25}\sqrt{13}\\[5pt] &= 5\sqrt{13}\,\textrm{.} \end{align} |
