Region on Complex Plane Without Modulus
Geometrically, $\operatorname{Re}(z)+\operatorname{Im}z=3$ is just the line $x+y=3$. And $|z-2-2i|=3$ is just the circle with center $(2,2)$ and radius $3$. So, you have the union of a line and a circle.
Region on Complex Plane Without Modulus
Geometrically, $\operatorname{Re}(z)+\operatorname{Im}z=3$ is just the line $x+y=3$. And $|z-2-2i|=3$ is just the circle with center $(2,2)$ and radius $3$. So, you have the union of a line and a circle.