# Homework Help: Complex numbers

1. Sep 10, 2010

### mynameisfunk

OK, in my book we have an inequality ||z|-|w||$$\leq$$|z+w|$$\leq$$|z|+|w| then from here it simply states, "Replacing w by -w here shows that ||z|-|w||$$\leq$$|z-w|$$\leq$$|z|+|w|.

How do we know that???
is |z+w|=|z-w|?? Note that z and w are complex numbers.

2. Sep 10, 2010

### Dick

No, |z+w| is NOT equal to |z-w|. Your first inequality is true for all w. Therefore it also must be true for -w. Substitute '-w' everywhere you see 'w' in the first inequality.

3. Sep 10, 2010

### mynameisfunk

Thanks alot Dick, again. You rock

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