$\lim _{z\rightarrow -i}\dfrac{1}{z-i}=\dfrac{i}{2}$ Why this answer?

Question

$i$ is imaginary number. I think this quiestion. $$\lim _{z\rightarrow -i}\dfrac{1}{z-i}=\dfrac{i}{2}$$ I think this answer is $-\dfrac{1}{2i}$.

I don't know why this answer is $\dfrac{i}{2}$. please tell me.

Answer 1

$$ -\frac{1}{2i} = -\frac{i}{(2i)i} = -\frac{i}{-2} = \frac{i}{2} $$