"I know that pilots and co-pilots must make some very complex calculations before take-off, as well as during flights."
Not really. It's just basic math. For those that still use pen & paper, the weight & balance is simple addition & subtraction. Many carriers now use computer tablets or operations figures these numbers for you. At the most complicated, only simple algebra is used to figure time/distance, fuel burn or descent problems in your head. The most common might be when you are given a descent with a navaid/fix crossing restriction at a certain altitude, so you need to know how many feet per minute to descend to make the restriction. X many feet to lose, at X airpseed, in x number of miles type thing. Plus, as many have pointed out, it's the norm for the FMS to do the simplest calculations these days. I took calculus and advanced math at ERAU and have never used them in the cockpit.
There is a great book on this subject called "Mental Math for Pilots" by Ronald McElroy. It has lots tips & trick to figure the most common mental math problems encountered in the airline environment. You can check it out at-