Discussion
Determine the order of the pole of \( \dfrac{1}{(z-1)^{3}} \) at \( z = 1 \).
Answer: A
The order of a pole is the power of the vanishing factor in the denominator, here three, so the Laurent expansion about \( z = 1 \) runs down to \( (z-1)^{-3} \) and no further. A first power would give a simple pole, and no finite power gives an essential singularity
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