Traditionally, vectors and complex numbers are treated in dedicated courses like vector calculus and complex analysis. For spaces of order three or higher, we must use vectors. Yet, most of the circuit analysis and synthesis involve two-dimensional vectors. As will be clear shortly, substituting complex analysis methods for vector analysis may prove handy and more inspiring. Secondly, complex analysis methods can readily handle trigonometric relations and identities. Trigonometric identities are used implicitly in the following sections. It is a good idea to refer to your related math notes involving complex analysis.