Hello, i got this question in a exam:
Get the Laurent Series of
$\displaystyle {\sqrt{(z-1)(z-2)}}$
i think he said we could do the expansion at the point of our choice
can you help me out?
Notice that $\displaystyle (z-1)(z-2) = z^2 - 3z + 2 = z^2 - 3z + \tfrac{9}{4} - \tfrac{9}{4} + 2 = \left( z - \tfrac{3}{2} \right)^2 + \tfrac{17}{4}$.
Thus, I think the most conveint point is $\displaystyle \tfrac{3}{2}$ to exand the series.
Now, you can almost finish the problem by applying the binomial series.