MHB Partial Fraction Decomposition of Complex Fractions

[Dustinsfl]

$$
\frac{1}{z^2(1-z)} = \frac{A}{z^2}+\frac{B}{1-z}
$$I can't figure out how to decompose this fraction.

 

[Chris L T521]

$$
\frac{1}{z^2(1-z)} = \frac{A}{z^2}+\frac{B}{1-z}
$$I can't figure out how to decompose this fraction.

You're missing a term. The decomposition should be of the form

\[ \frac{1}{z^2(1-z)} = \frac{A}{z}+\frac{B}{z^2}+\frac{C}{1-z} \]

Is it also to be assumed that $A,B,C\in\mathbb{C}$?