Lösung 3.2:4b

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We calculate what the expression will be
We calculate what the expression will be
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{{Displayed math||<math>(2-i)+(5+3i) = 2+5+(-1+3)i = 7+2i</math>}}
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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 calculate the magnitude,
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and then take the magnitude:
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{{Displayed math||<math>|7+2i| = \sqrt{7^2+2^2} = \sqrt{49+4} = \sqrt{53}\,\textrm{.}</math>}}
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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: It is not possible to calculate the magnitude of the terms individually
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{{Displayed math||<math>|(2-i)+(5+3i)| \ne |2-i| + |5+3i|\,\textrm{.}</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>
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Version vom 11:57, 29. Okt. 2008

We calculate what the expression will be

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

and then calculate the magnitude,

\displaystyle |7+2i| = \sqrt{7^2+2^2} = \sqrt{49+4} = \sqrt{53}\,\textrm{.}


Note: It is not possible to calculate the magnitude of the terms individually

\displaystyle |(2-i)+(5+3i)| \ne |2-i| + |5+3i|\,\textrm{.}
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.2:4b“