Is there an interval notation for complex numbers? Just as $$\{x \in \mathbb{R}:  a \leq  x \leq b\}$$ can be written in the more-compact form $[a,b],$ is there an analogous notation for $$\{z \in \mathbb{C}:z=x+yi, x \in[a,b], y \in[c,d]\} \quad ?$$
Pictorially, the set of all  $z \in \mathbb{C}$ lying in the green area is the set that I'd like to express in a more concise form:


As far as I know there is no widely recognized standard notation. Define one in your paper/book/essay if you need it often.
