Lösung 3.4:3

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A polynomial equation which has real coefficients always has complex conjugate roots. We can therefore say directly that the equation, in addition to the roots
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<center> [[Image:3_4_3.gif]] </center>
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<math>z=\text{2}i</math>
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and
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<math>z=-\text{1}+i</math>, has roots
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<math>z=\overline{2i}=-2i</math>
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and
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<math>z=\overline{-\text{1}+i}=-1-i</math>. Because the equation is of degree 4, it does not have more than 4 roots.
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The answer is thus
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<math>\left\{ \begin{array}{*{35}l}
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2i \\
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-2i \\
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-1+i \\
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-1-i \\
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\end{array} \right.</math>

Version vom 10:18, 28. Okt. 2008

A polynomial equation which has real coefficients always has complex conjugate roots. We can therefore say directly that the equation, in addition to the roots \displaystyle z=\text{2}i and \displaystyle z=-\text{1}+i, has roots \displaystyle z=\overline{2i}=-2i and \displaystyle z=\overline{-\text{1}+i}=-1-i. Because the equation is of degree 4, it does not have more than 4 roots.

The answer is thus


\displaystyle \left\{ \begin{array}{*{35}l} 2i \\ -2i \\ -1+i \\ -1-i \\ \end{array} \right.

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.4:3“