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Contradiction in the definition and properties of the abs

  1. Feb 16, 2014 #1
    If the abs(a+b) = abs(a) + abs(b), so the abs(z) = abs(x+iy) = abs(x) + abs(iy) = abs(x) + i abs(y). However, the correct wouldn't be abs(z) = √[x²+y²] ?

    √[x²+y²] ≠ abs(x) + i abs(y) => abs(z) ≠ abs(z)

    It's no make sense. What there is of wrong with those definions?
     
  2. jcsd
  3. Feb 16, 2014 #2

    PeroK

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    [tex]|a + b| \neq |a| + |b|[/tex]
    E.g. a = 2, b = -1
     
  4. Feb 16, 2014 #3

    Mark44

    Staff: Mentor

    As PeroK notes, this is incorrect. Since your hypothesis is false, any following work is meaningless.

    Also, the | key on the keyboard is usually used to write absolute values, as in |a + b|.
     
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