2. Let the function $f(z) = \frac{4-3z}{z^3 - 3z^2 + 2z}$. The poles of $f(z)$ are $z = 0, 1$ and $2$ which are simple poles. Given $C: |z| = \frac{3}{2}$ which represents a circle centered at 0 with a radius $\frac{3}{2}$.
a) Determine the poles that lie within C.
b) State the definition of residues. Hence, show that Res$(f, 0) = 2$ and Res$(f, 1) = -1$.
c) By using the Cauchy's Residue Theorem, show that $\int_C \frac{4-3z}{z^3 - 3z^2 + 2z} dz = 2\pi i$.