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f(z) = [tex]\frac{z^{1/2}}{z^{2}+1}[/tex]

I can see that the singular points are at z=i and z=-i but have no idea how to classify them or find the residue at each point.

I know finding the residue depends on if the singular points are removable singulairties, poles or zeros of certain orders but don't know to classify z=i or z=-i.

Any help would be brillant, thankyou.