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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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    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.
  4. Sep 10, 2010 #3
    Thanks alot Dick, again. You rock
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