TITLE: Complex Analysis Book with Good Exercises?
QUESTION [6 upvotes]: I have studied a bit of complex analysis in the past, but I realized that I couldn't really get into it because I didn't really see the motivation; I was spending a lot of time trying to understand proofs, and even though the theorems seemed pretty cool, I never really got to use them. Could you please recommend me some books with applications of Complex Analysis? I don't mean applications to science or engineering, I just mean applications of the theorems in first year Complex Analysis, aka a book with good, interesting problems, not necessarily a book with formal proofs of everything (though that's a bonus).
Thank you very much.

REPLY [4 votes]: If you are more into solving problems and applying mathematics you can't go wrong with J. W. Brown and R. V. Churchill, Complex Variables and Applications (currently at its 9th edition, I guess). An alternative would be M. J. Ablowitz and A. S. Fokas, Complex Variables, great if you want to do modern applied mathematics, especially nonlinear ODEs and PDEs.  Now, if you are more into pure mathematics I'd recommend R. B. Ash and W. P. Novinger Complex Variables, 2nd ed. (there is a cheap edition by Dover, but you can also legally download it, so it wouldn't hurt to take a glance).  An oldie but goldie alternative would be, of course, E. C. Titchmarsh, The Theory of Functions, 2nd ed. -- it's all there, clear cut, masterly exposed.  I don't like the textbooks by Ahlfors (dated, not very pedagogic, a little pedantic) or Conway (a mess), but maybe it's just me.