I need recommendation about complex analysis book. As I'm electrical engineering student, it should cover everything one engineer need to know about that mathematical field, but without strict mathematical formalism.
I would start with looking on MIT Open Course Ware. E.g., Complex Variables with Applications could be interesting for you. They use the book Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics by Saff and Snider, but you might find it sufficient to browse the lecture notes. This course might also be interesting for you.
Saff and Snider's Fundamentals of complex analysis is a nice enough book. It's just excessively pricey.
Brown & Churchill's Complex Variables and Applications is a good option as well (you can get an old edition for pretty cheap, and its content-wise the same as the new ones).
Marsden & Hoffman's Basic Complex Analysis is also a good option, but its a tiny bit more advanced than the other options (but still suitable for Eng/Math/Physics students). A nice feature of this is that he has a lot of hints and worked out problems.
The OCW courses linked in Matt L.'s answer are alright -- the second one is based around Ahlfors' book which is more advanced than what most EE's will need (and just has some extra stuff to supplement Ahlfors).
If I were to pick one, I'd go with Brown & Churchill as its the one I used as an undergraduate, with Marsden & Hoffman as a close second.
it should cover everything one engineer need to know about that mathematical field, but without strict mathematical formalism.
Off to the wrong start. Looking back, the important thing I was though in higher math for engineers was definetely how to understand, apply and transform mathematical formalisms.
Look at it this way: the difference between a tinkerer and an engineer is that the engineer understands its topic so deeply that he can sensibly design based on the inner workings, rather than on experience alone.
That is usually done using strict, mathematical formalisms.
I might be a bit on the hard side of this these days (I certainly wasn't during my first few semesters at university), but I really think that especially in a signal processing context, not knowing how to adhere to mathematical rigor is a recipe for disaster and handwaving.