http://ocw.mit.edu/OcwWeb/Mathematics/18-04Complex-Variables-with-ApplicationsFall1999/CourseHome/index.htm
Are you looking for an analysis or an applications course? Do you already understand the Cauchy residue theorem, and the Cauchy-Reimann equations?
Nope... Force vectors are the most common in your course. You can use vectors to describe velocity, but be sure not to mix them into your free-body diagrams.