Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
jsMath

Lösung 3.4:3

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K
Zeile 1: Zeile 1:
-
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
+
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.
-
<math>z=\text{2}i</math>
+
-
and
+
-
<math>z=-\text{1}+i</math>, has roots
+
-
<math>z=\overline{2i}=-2i</math>
+
-
and
+
-
<math>z=\overline{-\text{1}+i}=-1-i</math>. Because the equation is of degree 4, it does not have more than 4 roots.
+
The answer is thus
The answer is thus
-
 
+
{{Displayed math||<math>z = \left\{\begin{align}
-
<math>\left\{ \begin{array}{*{35}l}
+
&\phantom{+}2i\,,\\[5pt]
-
2i \\
+
&-2i\,,\\[5pt]
-
-2i \\
+
&-1+i\,,\\[5pt]
-
-1+i \\
+
&-1-i\,\textrm{.}
-
-1-i \\
+
\end{align} \right.</math>}}
-
\end{array} \right.</math>
+

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 z=2i and z=−1+i, has roots z=2i=−2i and z=−1+i=−1−i. Because the equation is of degree 4, it does not have more than 4 roots.

The answer is thus

z=2i−2i−1+i−1−i.
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.4:3“