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Lösung 3.1:1c

Aus Online Mathematik Brückenkurs 2

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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
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<math>\begin{align}i(2+3i)&=i\cdot 2+i\cdot 3i=2i+3i^2\\
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{{Displayed math||<math>\begin{align}
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&=2i+3\cdot (-1)=2i-3\\
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i(2+3i)
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&=-3+2i\end{align}</math>
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&= i\cdot 2 + i\cdot 3i\\[5pt]
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&= 2i+3i^2\\[5pt]
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&= 2i+3\cdot (-1)\\[5pt]
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&= 2i-3\\[5pt]
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&= -3+2i\,\textrm{.}
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\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 i2=−1. The distributivity rule gives that

i(2+3i)=i2+i3i=2i+3i2=2i+3(−1)=2i−3=−3+2i.
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.1:1c“