- #1

- 986

- 9

## Homework Statement

If x, y are complex, prove that

| |x| - |y| | ≤ |x - y|

## Homework Equations

If x = a + ib, |x| = √(a

^{2}+b

^{2})

|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?