I'm trying to find the residue at $0$ of the function
$f(z)=\frac{1+iz-e^{iz}}{z^3}$
on $\mathbb{C} - \{0\}$.
I think it's a double pole at the origin, but I'm not entirely sure. I'm wondering if it's best to try and find the Laurent expansion of the function on a suitable annulus, or whether there's a neater trick to find the residue.
Thanks in advance.