## Proving the complex Log function is not continuous

The question is:

Let $Log z = ln \left | z \right | + i \theta$ where $-\pi < \theta \leq \pi$and $z=\left | z \right | e^{i\theta}$, $(z\neq 0)$. Prove that Log is not continuous on $(- \infty,0).$

Hint: Consider the sequences {-1+i/n} and {-1-i/n}.

I am not sure how I should be using these sequences in the proof.