# Thread: Small question on order of poles

1. ## Small question on order of poles

If you have a function thats

f(z) = g(w)/(z^2-2i) and you want the residue at z = 1+i, z^2 = 2i and g(w) analytic at the point

would the order of the pole still be 1 even though its z^2?

or would this require the laurent series to determine properly?

thanks for any help

2. ## Re: Small question on order of poles

Originally Posted by Daniiel
If you have a function thats

f(z) = g(w)/(z^2-2i) and you want the residue at z = 1+i, z^2 = 2i and g(w) analytic at the point

would the order of the pole still be 1 even though its z^2?

or would this require the laurent series to determine properly?

thanks for any help
Well think about it, if you wanted to figure out the order of the ple at $z=1+i$ you need to figure out what is the minimum $n$ such that $\displaystyle \lim_{z\to 1+i}(z-(1+i))^n\frac{g(z)}{z^2-2i}$ exists.

3. ## Re: Small question on order of poles

g(w)/(z-(1+i))(z+(1+i)) n=1

I had troubling seeing that it could be split apart into that.

iz all good,

thanks! =]