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Lösung 3.2:2b

Aus Online Mathematik Brückenkurs 2

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<math>\begin{align}
<math>\begin{align}
0 &\leq \mathrm{Re}z \leq 1,\\
0 &\leq \mathrm{Re}z \leq 1,\\
-
0 &\leq \mathrm{Im}z \leq 1,\end{align}
+
0 &\leq \mathrm{Im}z \leq 1,\end{align}</math>
-
\mathrm{Re}z \leq \mathrm{Im}z.
+
<math>\mathrm{Re}z \leq \mathrm{Im}z
-
</math>
+
</math>.
The first two inequalities in this list define the unit square in the complex number plane.
The first two inequalities in this list define the unit square in the complex number plane.

Version vom 10:49, 3. Okt. 2008

The inequality 0RezImz1 is actually several inequalities:

00Rez1Imz1

RezImz.

The first two inequalities in this list define the unit square in the complex number plane.

The last inequality says that the real part of z should be less than or equal to the imaginary part of z, I.e. z should lie to the left of the line y=x if x=Rez and y=Imz.

All together, the inequalities define the region which the unit square and the half-plane have in common: a triangle with corner points at 0, i and 1+i.

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.2:2b“