1. ## poles

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

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

any tips?

found it online