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Triangle inequality

  1. Sep 9, 2010 #1
    My problem states:
    Given z, w[tex]\in[/tex]C, prove: ||z|-|w||[tex]\leq[/tex]|z-w|[tex]\leq[/tex]|z|+|w|.

    Now, I am confused because, isn't it true that ||z|-|w||=|z-w| ? I am using Rudin's book which gives |z|=([z's conjugate]z)1/2
     
  2. jcsd
  3. Sep 9, 2010 #2
    Take z =-2 and w = 2. Does ||z|-|w||=|z-w| still hold?
     
  4. Sep 9, 2010 #3
    Ah. Thank you. Is it correct from the definition of |z| to think of it as a length? My gf is taking a complex variables class and she had told me that |z|= the length of z, but rudin's book gave the definition above, so i didn't know how to think about it.
     
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