Lösung 3.2:4a

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The magnitude of the number
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<center> [[Image:3_2_4a.gif]] </center>
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<math>\text{3}+\text{4}i</math>
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is the number's distance to the origin in the complex number plane.
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If we treat the line from the origin to
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<math>\text{3}+\text{4}i</math>
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as the hypotenuse in a right-angled triangle which has its sides parallel with the real and imaginary axes, then Pythagoras' theorem gives that the magnitude is
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<math>\left| \text{3}+\text{4}i \right|=\sqrt{3^{2}+4^{2}}=\sqrt{9+16}=\sqrt{25}=5</math>
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[[Image:3_2_4_a.gif|center]]
[[Image:3_2_4_a.gif|center]]
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NOTE: In general, the magnitude of a complex number
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<math>z=x+iy</math>
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is equal to
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<math>\left| z \right|=\left| x+iy \right|=\sqrt{x^{2}+y^{2}}</math>

Version vom 15:19, 22. Okt. 2008

The magnitude of the number \displaystyle \text{3}+\text{4}i is the number's distance to the origin in the complex number plane.

If we treat the line from the origin to \displaystyle \text{3}+\text{4}i as the hypotenuse in a right-angled triangle which has its sides parallel with the real and imaginary axes, then Pythagoras' theorem gives that the magnitude is


\displaystyle \left| \text{3}+\text{4}i \right|=\sqrt{3^{2}+4^{2}}=\sqrt{9+16}=\sqrt{25}=5


NOTE: In general, the magnitude of a complex number \displaystyle z=x+iy is equal to


\displaystyle \left| z \right|=\left| x+iy \right|=\sqrt{x^{2}+y^{2}}

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