Lösung 3.2:4c

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One way to determine the magnitude is to calculate the product
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<center> [[Image:3_2_4c.gif]] </center>
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<math>\left( \text{3}-\text{4}i \right)\left( \text{3}+\text{2}i \right)</math>
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and then to take the magnitude of the result, but for products
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<math>\left| zw \right|=\left| z \right|\centerdot \left| w \right|</math>
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and we can take the magnitude of the factors
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<math>\text{3}-\text{4}i</math>
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and
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<math>\text{3}+\text{2}i</math>
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and then multiply the magnitudes together:
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<math>\begin{align}
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& \left| \left( \text{3}-\text{4}i \right)\left( \text{3}+\text{2}i \right) \right|=\left| \left( \text{3}-\text{4}i \right) \right|\centerdot \left| \left( \text{3}+\text{2}i \right) \right| \\
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& =\sqrt{3^{2}+\left( -4 \right)^{2}}\centerdot \sqrt{3^{2}+2^{2}} \\
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& =\sqrt{9+16}\centerdot \sqrt{9+4} \\
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& =\sqrt{25}\centerdot \sqrt{13}=5\sqrt{13} \\
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\end{align}</math>

Version vom 15:33, 22. Okt. 2008

One way to determine the magnitude is to calculate the product \displaystyle \left( \text{3}-\text{4}i \right)\left( \text{3}+\text{2}i \right) and then to take the magnitude of the result, but for products


\displaystyle \left| zw \right|=\left| z \right|\centerdot \left| w \right|


and we can take the magnitude of the factors \displaystyle \text{3}-\text{4}i and \displaystyle \text{3}+\text{2}i and then multiply the magnitudes together:


\displaystyle \begin{align} & \left| \left( \text{3}-\text{4}i \right)\left( \text{3}+\text{2}i \right) \right|=\left| \left( \text{3}-\text{4}i \right) \right|\centerdot \left| \left( \text{3}+\text{2}i \right) \right| \\ & =\sqrt{3^{2}+\left( -4 \right)^{2}}\centerdot \sqrt{3^{2}+2^{2}} \\ & =\sqrt{9+16}\centerdot \sqrt{9+4} \\ & =\sqrt{25}\centerdot \sqrt{13}=5\sqrt{13} \\ \end{align}

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