Sequence of Imaginary Reciprocals/Closure is Compact

Theorem
The closure $S^-$ of the set $S$ is compact.

Proof
From Topological Closure is Closed, $S^-$ is closed.

From Sequence of Imaginary Reciprocals: Boundedness, $S$ is bounded in $\C$.

It follows trivially that $S^-$ is also bounded in $\C$.

Hence the result by definition of compact.