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a past exam question asked me to find and classify the residues of this.

i had to factorise it into this form and then i just said there was a double pole at [itex]z=+i,z=-i[/itex]

now for 5 marks, this doesn't seem like very much work.

is it possible to perform a laurent expansion and then show explicitly that they are poles of order 2 rather than just saying "the power of the brackets is 2 and so it must be of order 2"?