I am doing a project about irrational and transcendental numbers and part of this project involves looking at sums and products of various combinations of rational, irrational, algebraic and transcendental numbers. I am quite happy that I have done what I need to with rational and irrational numbers however I need help with algebraic and transcendental numbers
I need to find out and prove what the solutions of the following are: 1) algebraic + algebraic 2) algebraic + transcendental 3) transcendental + transcendental 4) algebraic x algebraic 5) algebraic x transcendental 6) transcendental x transcendental
Also if there are any interesting results from sums and products of (ir)rationals with algebraic or transcendental numbers then these would be of great help too.
Any help is greatly appreciated, and thanks in advance.