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[SOLVED] Complex partial fractions

dwsmith

Well-known member
Feb 1, 2012
1,673
$$
\frac{1}{z^2(1-z)} = \frac{A}{z^2}+\frac{B}{1-z}
$$


I can't figure out how to decompose this fraction.
 

Chris L T521

Well-known member
Staff member
Jan 26, 2012
995
$$
\frac{1}{z^2(1-z)} = \frac{A}{z^2}+\frac{B}{1-z}
$$


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 $A,B,C\in\mathbb{C}$?