I found this useful: What Is Complex Analysis?

Course Guidance, Johns Hopkins University Math Department - click for "What is Linear Algebra" etc

Because seeing the forest sometimes helps you see the trees.
I spent a couple of hours on such summaries and also on several related wikipedia entries (the field, its applications, its origins) as well as mathworld/mathematica entries.

Getting a panoramic scope of the math helps.  In this case, the histories and human stories - Euler, Gauss, Riemann, ...; the connections to the future via modern physics research and prominent math research prizes, or to popularly-used industry and engineering solutions (the present), or merely as artifacts (the past) - all of these add colour and motivate the learner to slog through the textbook exposition and exercises if necessary, or to skip and simply enjoy the knowledge of the forest without a visit to the trees. 

I feel good about my short investment in getting these varied overviews on Complex Analysis.
May it help me turn the corner on this little subject, for which it's strangely true that although I've worked several examples and taken a couple of courses in it, I just don't (didn't?) "really" understand it beyond the Cauchy-Riemann equations.  This is not the same as saying that I haven't solved questions correctly; it's just that I then forget how, which proves that I never really believed the solution paradigm maybe?

Complex Variables and related webpages - This was breakfast

And as for the strategy of grazing material about a topic in a general-interest fashion, I will reuse that and see how it helps me tackle Tensors, and Multivariable Calculus, and theories of PDEs, where I still have sizeable gaps in understanding, largest of all with Tensors I think.