Laurent expansion of $\frac{1}{z^2+i}$ at $z=i$

Question

I want to find the Laurent series of $1\over(z^2+i)$at $z=i$. How do I start and go on from there? Do I start with either of these?

$$1 \over{(z+i\sqrt i)(z-i\sqrt i)}$$

$$\frac{1}{i} \frac{1}{1+(z^2/i)}$$

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