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:


Since $\mathbb C$ is just $\mathbb R^2$ with specific operations, the notation $[a,b]\times[c,d]$ obviously do the trick. 
