I am analyzing a function $f(x+jy)$ in the complex plane, and it is differentiable if and only if $x = 0$ or $y = 0$, i.e. it is differentiable on the imaginary and real axes. What would be the proper way to then denote the domain on which the function is differentiable?
My intuition says that I can state the domain of the derivative as $\mathbb{R} \cup \mathbb{I}$ , i.e. $z$ is an element of either the set of reals or the set of imaginaries.
Is this the correct notation? Or is there a more appropriate way to state the domain?
I appreciate the assistance, thank you!