I'm having trouble determining the order of the pole of(adsbygoogle = window.adsbygoogle || []).push({});

[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?)

thanks for your help.

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# Order of poles

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