Lösung 3.2:4c

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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
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{{Displayed math||<math>|zw| = |z|\cdot |w|</math>}}
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{{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}
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{{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 \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}

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.2:4c“