Ok hi guys, I'm in a lot of trouble with my maths teacher, and it seems like the only thing that can help my grades would be solving three problems from a math magazine that gets published around here. I have scanned them and I will provide a translation so you can have an idea of the goals.

**First problem**: ABCD is a convex quadrilater. E is the middle of the AC diagonal; F is the middle of the BD diagonal; M is a randomly chosen point. Demonstrate that : ...

**Second problem**emonstrate that the following is true for any z1, z2, z3 complex numbers.

**Third problem**: Determine the (an)n>=0 strings of numbers knowing that the following is true for any n natural number.

**Fourth problem**: knowing that z1 and z2 are complex numbers with the same modulus, prove the following:....

If you can solve any of these, I would be very thankful