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The following function :

a) [tex] f(z) = \frac{1}{z^6 + 1} [/tex]

has simple poles on :

[tex] z_1 = e^{pi/6 i}, z_2 = e^{3pi/6 i}, z_3 = e^{5pi/6 i} [/tex]

I know how to get the poles, but how could I demonstrate they are simple (order 1) ?

I tried to write the Laurent series centered in the pole, but I got nowhere...

Is there any general way to determine the order of a pole without using Laurent ?

Thanks.

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# Homework Help: Contour Integral: how to get the order of those poles?

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