Lösung 3.2:4b

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We calculate what the expression will be
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<center> [[Image:3_2_4b.gif]] </center>
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<math>\left( 2-i \right)+\left( 5+3i \right)=2+5+\left( -1+3 \right)i=7+2i</math>
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and then take the magnitude:
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<math>\left| 7+2i \right|=\sqrt{7^{2}+2^{2}}=\sqrt{49+4}=\sqrt{53}</math>
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NOTE: Note that it is not possible to take the magnitude of the terms individually
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<math>\left| \left( 2-i \right)+\left( 5+3i \right) \right|\ne \left| 2-i \right|+\left| 5+3i \right|</math>

Version vom 15:25, 22. Okt. 2008

We calculate what the expression will be


\displaystyle \left( 2-i \right)+\left( 5+3i \right)=2+5+\left( -1+3 \right)i=7+2i

and then take the magnitude:


\displaystyle \left| 7+2i \right|=\sqrt{7^{2}+2^{2}}=\sqrt{49+4}=\sqrt{53}


NOTE: Note that it is not possible to take the magnitude of the terms individually


\displaystyle \left| \left( 2-i \right)+\left( 5+3i \right) \right|\ne \left| 2-i \right|+\left| 5+3i \right|

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