Lösung 3.2:1b
Aus Online Mathematik Brückenkurs 2
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Version vom 10:34, 11. Mär. 2009
We can easily calculate \displaystyle z+u and \displaystyle z-u,
| \displaystyle \begin{align}
z+u &= 2+i+(-1-2i) = 2-1+(1-2)i = 1-i,\\[5pt] z-u &= 2+i-(-1-2i) = 2+1+(1+2)i = 3+3i, \end{align} |
and then mark them on the complex plane.
An alternative is to view \displaystyle z and \displaystyle u as vectors and \displaystyle z+u as a vector addition of \displaystyle z and \displaystyle u.
We can either view the vector subtraction \displaystyle z-u as \displaystyle z+(-u),
or interpret \displaystyle z-u from the vector relation
| \displaystyle z=(z-u)+u\,, |
i.e. \displaystyle z-u is the vector we add to \displaystyle u to arrive at \displaystyle z.
