(adsbygoogle = window.adsbygoogle || []).push({}); The problem

Find Res(f,z1)

With: [itex]f(z)=\frac{z}{(z^2+2aiz-1)^2}[/itex]

The attempt at a solution

The singularities are at [itex]A=i(-a+\sqrt{a^2-1})[/itex] and at [itex]B=i(-a-\sqrt{a^2-1})[/itex]

With the normal equation (take limit z->A of [itex]\frac{d}{dz}((z-A)^2 f(z))[/itex] for finding the residue of a pole of order 2, my attempt fails.

I know the way the correct answer is constructed, but I do not understand it.

The solution is namely: take [itex]\frac{d}{dz}[/itex] of [itex]\frac{z}{(z-B)^2}[/itex]

This is: [itex]\frac{-(z+B)}{(z-B)^3}[/itex]

Then plug in z=A, which gives: [itex]\frac{-(A+B)}{(A-B)^3}[/itex]

Now plugging in the values of A and B give the correct answer.

Any help is appreciated.

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# Homework Help: Finding the residue of a pole of order 2 (complex analysis)

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