Are you asking what the pre-req's are? Or are you asking how to learn some fundamental techniques from complex analysis without taking complex analysis?
the basic ideas in complex analysis are path integration, infinite series (including negative powers), plane topology, and explicit angle preserving ("conformal") transformations defined by linear fractional transformations of form (az+b)/cz+d) which take lines and circles into lines and/or circles. you could study any of these.