# 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

### Office_Shredder

Staff Emeritus
You can choose any number for w. In particular, -w works too. The key is that |-w|=|w|

3. Sep 11, 2010

### HallsofIvy

No, |z+w| is not equal to |z- w| and it doesn't say that. "Replacing w by -w" changes |z+ w| to |z+ (-w)|= |z- w|. And, as Office_Shredder said, |-w|= |w| whether w is real or complex.

4. Sep 11, 2010

### mynameisfunk

Thanks guys, I get it now. I very much appreciate the help, as always.