Answer to Question #227038 in Complex Analysis for smi

Question

Find the closure of the following set in C

{z∈C : (ReZ)²=ImZ}

Answer 1

The set is a curve in $\mathbb{C}$. Thus, it is closed, since the set coincides with its boundary. Since the set is closed, the closure of the set is the set itself, i.e., $\{z\in{\mathbb{C}}:(Re z)^2=Im z\}$.