Lösung 3.1:1c

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K
Zeile 1: Zeile 1:
-
{{NAVCONTENT_START}}
 
Complex numbers satisfy the same rules of arithmetic as ordinary numbers, with the addition that <math>i^2=-1</math>. The distributivity rule gives that
Complex numbers satisfy the same rules of arithmetic as ordinary numbers, with the addition that <math>i^2=-1</math>. The distributivity rule gives that
-
<math>\begin{align}i(2+3i)&=i\cdot 2+i\cdot 3i=2i+3i^2\\
+
{{Displayed math||<math>\begin{align}
-
&=2i+3\cdot (-1)=2i-3\\
+
i(2+3i)
-
&=-3+2i\end{align}</math>
+
&= i\cdot 2 + i\cdot 3i\\[5pt]
-
{{NAVCONTENT_STOP}}
+
&= 2i+3i^2\\[5pt]
 +
&= 2i+3\cdot (-1)\\[5pt]
 +
&= 2i-3\\[5pt]
 +
&= -3+2i\,\textrm{.}
 +
\end{align}</math>}}

Version vom 14:49, 29. Okt. 2008

Complex numbers satisfy the same rules of arithmetic as ordinary numbers, with the addition that \displaystyle i^2=-1. The distributivity rule gives that

\displaystyle \begin{align}

i(2+3i) &= i\cdot 2 + i\cdot 3i\\[5pt] &= 2i+3i^2\\[5pt] &= 2i+3\cdot (-1)\\[5pt] &= 2i-3\\[5pt] &= -3+2i\,\textrm{.} \end{align}

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.1:1c“