For real number search problems, the binary search algorithm is the go-to method. Yet, the answer becomes not so obvious when considering searching for some number $x$ such that $|x-Z_0|\leq R$.
I want to know if there is any study for searching in the complex plane. Some questions are: I) Is there a counterpart in such cases similar to the binary search? II) Is there concluding that the algorithm with the optimal computational complexity is found?