Two closed paths ${\gamma }_1,{\gamma }_2$ in $U$ are called Homologous in $U$, we write ${\gamma }_1\sim {\gamma }_2$ if they 1;;have the same winding number. That is, for each $a\in \mathbb{C}-U$, we have $n_{{\gamma }_1}(a)=n_{{\gamma }_2}(a)$.