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Complex numbers

  1. Sep 10, 2010 #1
    OK, in my book we have an inequality ||z|-|w||[tex]\leq[/tex]|z+w|[tex]\leq[/tex]|z|+|w| then from here it simply states, "Replacing w by -w here shows that ||z|-|w||[tex]\leq[/tex]|z-w|[tex]\leq[/tex]|z|+|w|.

    How do we know that???
    is |z+w|=|z-w|?? Note that z and w are complex numbers.
  2. jcsd
  3. Sep 10, 2010 #2


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    You can choose any number for w. In particular, -w works too. The key is that |-w|=|w|
  4. Sep 11, 2010 #3


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    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.
  5. Sep 11, 2010 #4
    Thanks guys, I get it now. I very much appreciate the help, as always.
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