Lösung 3.2:5a

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The argument of a complex number is angle of the line between the origin and the number measured with respect the positive real number axis.
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The argument of a complex number is the angle of the line between the origin and the number measured with respect the positive real number axis.
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In this case, we see directly that
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<math>-\text{1}0</math>
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has the argument
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<math>\pi </math>.
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In this case, we see directly that <math>-10</math> has the argument <math>\pi</math>.
[[Image:3_2_5_a.gif|center]]
[[Image:3_2_5_a.gif|center]]
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NOTE: All angles that correspond to the same direction differ by a whole number of turns, i.e. a multiple of
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Note: All angles that correspond to the same direction differ by a whole number of turns, i.e. a multiple of <math>2\pi</math>, and therefore we could have just as well answered <math>-\pi</math>, <math>3\pi</math>, <math>5\pi</math> etc. However, it is usual to give the argument between <math>0</math> and <math>2\pi</math> or between <math>-\pi</math> and <math>\pi</math>.
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<math>2\pi </math>, and therefore we could have just as well answered
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<math>-\pi </math>,
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<math>3\pi </math>,
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<math>5\pi </math>
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etc. However, it is usual to give the argument between
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<math>0</math>
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and
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<math>2\pi </math>
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or between
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<math>-\pi </math>
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and
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<math>\pi </math>.
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Version vom 12:25, 29. Okt. 2008

The argument of a complex number is the angle of the line between the origin and the number measured with respect the positive real number axis.

In this case, we see directly that \displaystyle -10 has the argument \displaystyle \pi.


Note: All angles that correspond to the same direction differ by a whole number of turns, i.e. a multiple of \displaystyle 2\pi, and therefore we could have just as well answered \displaystyle -\pi, \displaystyle 3\pi, \displaystyle 5\pi etc. However, it is usual to give the argument between \displaystyle 0 and \displaystyle 2\pi or between \displaystyle -\pi and \displaystyle \pi.

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.2:5a“