Order of poles

1. Mar 27, 2006

sachi

I'm having trouble determining the order of the pole of

[exp(iz) - 1]/((z^2) + 4) at z=2i

I know I can't just expand the exponential as 1 + iz + [(iz)^2]/2 .......
because this formula only works near the origin. Can I still use Taylor's theorem to find the expansion at z=2i (i.e does Taylor's theorem still work for complex variables?)