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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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 <math>z=2i</math> and <math>z=-1+i</math>, has roots <math>z=\overline{2i}=-2i</math> and <math>z=\overline{-1+i}=-1-i</math>. Because the equation is of degree 4, it does not have more than 4 roots.
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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
The answer is thus
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{{Displayed math||<math>z = \left\{\begin{align}
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<math>\left\{ \begin{array}{*{35}l}
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&\phantom{+}2i\,,\\[5pt]
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2i \\
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&-2i\,,\\[5pt]
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-2i \\
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&-1+i\,,\\[5pt]
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-1+i \\
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&-1-i\,\textrm{.}
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-1-i \\
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\end{align} \right.</math>}}
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\end{array} \right.</math>
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Version vom 13:29, 31. 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=2i and \displaystyle z=-1+i, has roots \displaystyle z=\overline{2i}=-2i and \displaystyle z=\overline{-1+i}=-1-i. Because the equation is of degree 4, it does not have more than 4 roots.

The answer is thus

\displaystyle z = \left\{\begin{align}

&\phantom{+}2i\,,\\[5pt] &-2i\,,\\[5pt] &-1+i\,,\\[5pt] &-1-i\,\textrm{.} \end{align} \right.

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