If x, y are complex, prove that
| |x| - |y| | ≤ |x - y|
If x = a + ib, |x| = √(a2+b2)
|x + y| ≤ |x| + |y| (works for both complex and real numbers)
The Attempt at a Solution
Maybe start with the left side
| |x| - |y| | = | |x| + (-|y|) | ≤ |x| + |-|y|| = |x| + |y|
....... Maybe almost there is I can show |x| + |y| ≤ |x - y| ........
How can I not get this problem?