Modulus of a complex number proving |s - t| ≥ |s| - |t| algebraically

[burgerandcheese]

This came after learning |s| = √(ss*)
How do I continue from here? Is there a way to factorise the last line? Is there a better way of doing this?

 

[pka]

This in the easiest of all complex number proofs.
We know that \(\displaystyle 0\le |z+w| \le |z|+|w|\) the triangle inequality.

So \(\displaystyle |s|=|s-t+t|\le|s-t|+|t|\) now subtract \(\displaystyle |t|\) to get
\(\displaystyle |s|-|t|\le |s-t|\).