Lösung 3.1:1d

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K (Lösning 3.1:1d moved to Solution 3.1:1d: Robot: moved page)
Zeile 1: Zeile 1:
{{NAVCONTENT_START}}
{{NAVCONTENT_START}}
-
<center> [[Image:3_1_1d.gif]] </center>
+
We expand the expression by multiplying each term in the first bracket with every term in the second bracket:
 +
 
 +
<math>\begin{align}(3-2i)(7+5i)&=3\cdot 7 + 3 \cdot 5i + \cdots\\
 +
&=3\cdot 7 + 3 \cdot 5i-2i\cdot 7 -2i \cdot 5i.\end{align}</math>
 +
 
 +
Then, we use that <math>i^2=-1</math> and write the real and imaginary parts together:
 +
 
 +
<math>\begin{align}(3-2i)(7+5i)&=21+15i-14i-10i^2\\
 +
&=21+15i-14i-10\cdot(-1)\\
 +
&=(21+10)+(15i-14i)\\
 +
&=31+1i\\
 +
&=31+i\end{align}</math>
 +
 
{{NAVCONTENT_STOP}}
{{NAVCONTENT_STOP}}

Version vom 11:51, 18. Sep. 2008

We expand the expression by multiplying each term in the first bracket with every term in the second bracket:

\displaystyle \begin{align}(3-2i)(7+5i)&=3\cdot 7 + 3 \cdot 5i + \cdots\\ &=3\cdot 7 + 3 \cdot 5i-2i\cdot 7 -2i \cdot 5i.\end{align}

Then, we use that \displaystyle i^2=-1 and write the real and imaginary parts together:

\displaystyle \begin{align}(3-2i)(7+5i)&=21+15i-14i-10i^2\\ &=21+15i-14i-10\cdot(-1)\\ &=(21+10)+(15i-14i)\\ &=31+1i\\ &=31+i\end{align}

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