Per the title, what are some of the oldest complex analysis books out there with (unsolved) exercises? Maybe there are some hidden gems from before the 20th century out there. I am aware of the classic books of Goursat and Titchmarsh.
It seems the first textbook on complex analysis was J.C. Bouquet and C.A. Briot, 1859, Théorie des fonctions doublement periodiques et, en particulier, des fonctions elliptiques
source: The Real and the Complex: A History of Analysis in the 19th Century
This 1859 text contains "examples", but no unsolved exercises. An early 20th century textbook with unsolved exercises is Theory of functions of a complex variable by H.F. Burkhardt. The book is from 1897, the exercises were added in 1913 by S.E. Rasor.

1
One of the first English complex analysis books with (unsolved) exercises was Whittaker and Watson, Course of Modern Analysis. First edition was published in 1902 (by E. T. Whittaker only). The exercises (more than 1000 of them) are mostly taken from the famous Cambridge Tripos exams. Some of them are very hard.
This book is famous for other reasons too: Old books still used
Remark. It seems to be an EnglishAmerican custom to include exercises in textbooks. In other languages (Russian, French) they don't include them, and publish separate books of exercises.

$\begingroup$ What are some of the earliest complex analysis exercise books in Russian and French, then? $\endgroup$ – Get Off The Internet Mar 6 at 12:19

$\begingroup$ In Russian, there are essentially two of them: by Volkovyskii MR0265563 (there is an English transl. in Dover) and by Evgrafov MR0262468, both published in 1960s. They are both rich sources and can be used not only as problem books but also as handbooks. $\endgroup$ – Alexandre Eremenko Mar 6 at 13:36

$\begingroup$ In French I know Exercises d'Analyse by Gaston Julia, 4 volumes, first edition 1933 $\endgroup$ – Alexandre Eremenko Mar 6 at 13:40

$\begingroup$ Before 1960s the Russians used Gunter and Kuzmin, Problems in Higher mathematics which covered all Analysis (and more), like the French book by Julia. I am not sure about the date of the first Russian edition, but it must be in 1930s. $\endgroup$ – Alexandre Eremenko Mar 6 at 13:44

$\begingroup$ In German, we have the famous PolyaSzego Problems and Theorems, which covers all Analysis, and specially for Complex Analysis, the books by Knopp (1923). $\endgroup$ – Alexandre Eremenko Mar 6 at 13:46