# Thread: Taylor/ Laurent series expansion question

1. ## Taylor/ Laurent series expansion question

Hi, im having much confusion and difficulty in answering this question.Thankyou for any help in advance

Let f be defined by

$f(z)=\frac{1}{2z^{2}-(1+2i)z+i}$

(a) Find the poles z1 and z2 of f such that $\left | z1 \right |< \left | z2 \right |$.
(b) Give the series expansion of f in the following three regions, stating in each case if it is a Taylor or Laurent series.
i. $\left | z \right |< \left | z1 \right |$
ii. $\left |z1 \right |< \left | z \right |< \left | z2 \right |$
iii. $|z-z1| < |z2-z1|$

Thankyou again.

2. To find the poles, set the denominator equal to $0$.

i.e. solve $\displaystyle{2z^{2}-(1+2i)z+i=0}$