1. The problem statement, all variables and given/known data Our teacher said we can try to prove that the complex numbers will only work so that they are an extension to real numbers if i=sqr(-1). 2. Relevant equations We know that |i|=1, and that for any complex numbers |a||b|=|ab|, and of course that the complex numbers are commutative, associative, and distributive. 3. The attempt at a solution I didn't have much ideas of how to prove this, I figured I need to try proving i^2=-1, so denoting u for the real number 1 unit, I wrote |u+i||u-i|=|u^2-i^2|, knowing that |u|=|i|=1 we can write sqr(2)*sqr(2)=|u^2-i^2|, and so 2=|1-i^2|. And from here, since |i|=1 and so |i*i|=1, the only way this can be is if i^2 = -1 and so i=sqr(-1). Is this an entirely precise and complete proof or did I miss something?