(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If x, y are complex, prove that

| |x| - |y| | ≤ |x - y|

2. Relevant equations

If x = a + ib, |x| = √(a^{2}+b^{2})

|x + y| ≤ |x| + |y| (works for both complex and real numbers)

3. 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?

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# Homework Help: Prove ||x|-|y||≤|x-y|, where x and y are complex

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