Reddit reviews Complex Variables: Second Edition (Dover Books on Mathematics)

I liked my textbook. It's not advanced, but it does have proofs. It's accessible to engineers.

Complex Variables by Stephen D. Fisher


If you don't mind learning some history too, then An Imaginary Tale is excellent. My professor recommended it when I took Complex Analysis. Also, there is a nice appendix that covers the basics of Complex Analysis at the end of Gamma by Havil. The Road to Reality is good.