Lösung 3.2:2b

The inequality \displaystyle 0\leq \mathrm{Re}z \leq \mathrm{Im}z \leq 1 is actually several inequalities:

\displaystyle \begin{align} 0 &\leq \mathrm{Re}z \leq 1,\\ 0 &\leq \mathrm{Im}z \leq 1,\end{align}

\mathrm{Re}z \leq \mathrm{Im}z.

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 \displaystyle z should be less than or equal to the imaginary part of \displaystyle z, I.e. \displaystyle z should lie to the left of the line \displaystyle y=x if \displaystyle x=\mathrm{Re} z and \displaystyle y = \mathrm{Im} z.

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