Plotting complex inequalities in maple

Question

I'm having trouble plotting a set of complex numbers in maple. I'm trying to plot the set

$$S = \lbrace z \in \Bbb C : 1 \leq \lvert z\rvert \leq 2, \frac{\pi}{4} \leq \lvert \arg(z)\rvert \leq \frac{\pi}{2}\rbrace.$$

I know what it should look like from a drawing I produced but I'd like to plot it in maple. My code is as follows;

z := x + I*y;

plots:-implicitplot([abs(z) <= 2, abs(z) <= 1, abs(arg(z)) >= Pi/4,
                     abs(arg(z)) <= Pi/2], x = -3...3, y = -3...3, filled = true);

The issue is that the inequalities are being plotted independently of each other rather than all together, so even the first pair of inequalities together fill the entire plane. Is there any way I can have the $4$ conditions imposed in $S$ be taken into account at the same time, rather than separately?

Answer 1

restart;

z := x + I*y:

plots:-implicitplot( piecewise( (abs(z) <= 2) and (abs(z) >= 1)
                                and (abs(argument(z)) >= Pi/4)
                                and (abs(argument(z)) <= Pi/2),
                                false, true),
                     x=-3...3, y=-3...3,
                     gridrefine=3, view=[-3..3,-3..3] );