If x, y are complex, prove that
||x| - |y|| < = |x - y|
For all, ,
Thus,
Thus,
Thus, adding same quality to both sides,
Thus,
Thus, take square root (note terms are non-negative),
--> Cauchy-Swartchz
--------------
Assume, then,
Thus,
Thus, adding same quality to both sides,
Thus,
Take square roots, (note terms are non-negative),
This is,
if,
I did not yet complete the proof when,
I do not see how