Is this a complex analysis course, or is it something that had complex analysis as a prerequisite?
Practically, to calculate these you can often do standard Taylor series calculations
[tex]f(x)=\frac{x}{1x} = \frac{1}{11/x}[/tex]
we know how to expand 1/(11/x) using the Taylor series for 1/(1x)
[tex] f(x) = 1+\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3}+...[/tex]
and this is valid as long as x>1
