# Math Help - poles

1. ## poles

let $D\subset \mathbb{C}$ be open, let $f\to\mathbb{C}" alt="f\to\mathbb{C}" /> be holomorphic, and let $z_0 \epsilon \mathbb{C}D$ be a zero of order one of $f$. Show that
res $(\frac{1}{f};z_0)=\frac{1}{f'(z_0)}$

let $D\subset \mathbb{C}$ be open, let $f\to\mathbb{C}" alt="f\to\mathbb{C}" /> be holomorphic, and let $z_0 \epsilon \mathbb{C}D$ be a simple pole for $f$. Show that
$res(gf;z_0)=g(z_0)res(f;z_0)$
for every holomorphic function $g\cup z_0 \to \mathbb{C}" alt="g\cup z_0 \to \mathbb{C}" />

any tips?

found it online