So I've just proven $|z_1+z_2|\le |z_1|+|z_2|$
and then I proved
if $a=z_1+z_2$ and $b=z_2$ then $||a|-|b||\le|a-b|$
And now I have to prove the following:
You can see that the top half is the triangle inequality... but then the bottom is the opposite of the second thing I had to prove. I had a friend that can prove this, only if it's based on the fact that $C\gt D$ but she didn't prove it in the other case where $D\gt C$ so I don't understand what to do.