4.I.8B

Complex Methods
Part IB, 2003

Find the Laurent series centred on 0 for the function

f(z)=1(z1)(z2)f(z)=\frac{1}{(z-1)(z-2)}

in each of the domains (a) z<1|z|<1, (b) 1<z<21<|z|<2, (c) z>2|z|>2.