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Lösung 3.1:1e

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
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K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel))
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A suitable first step can be to work out the square term, <math>(2-i)^2</math>, by expanding it,
A suitable first step can be to work out the square term, <math>(2-i)^2</math>, by expanding it,
-
{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
(2-i)^2 &= 2^2 - 2\cdot 2i + i^2\\[5pt]
(2-i)^2 &= 2^2 - 2\cdot 2i + i^2\\[5pt]
&= 4-4i+i^2\\[5pt]
&= 4-4i+i^2\\[5pt]
Zeile 10: Zeile 10:
After that, we calculate the remaining product,
After that, we calculate the remaining product,
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{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
(1+i)(3-4i) &= 1\cdot3 - 1\cdot 4i + i\cdot 3 - i\cdot 4i\\[5pt]
(1+i)(3-4i) &= 1\cdot3 - 1\cdot 4i + i\cdot 3 - i\cdot 4i\\[5pt]
&= 3-4i+3i-4i^2\\[5pt]
&= 3-4i+3i-4i^2\\[5pt]

Version vom 13:05, 10. Mär. 2009

A suitable first step can be to work out the square term, (2−i)2, by expanding it,

(2−i)2=22−22i+i2=4−4i+i2=4−4i−1=3−4i.

After that, we calculate the remaining product,

(1+i)(3−4i)=13−14i+i3−i4i=3−4i+3i−4i2=3+(−4+3)i−4(−1)=3−i+4=7−i.
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.1:1e“