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Help with a Math term

  1. Jun 29, 2008 #1
    What does it mean when an algebraic variable has a dash above it? _
    ---------------------------------------------------------------->z, like that?
     
  2. jcsd
  3. Jun 29, 2008 #2

    Hurkyl

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    Sometimes it's just used as a decoration to create a new alphabetic symbol to use. (there aren't enough alphabets for the purposes of mathematics!)

    Sometimes it's used to denote the complex conjugate function: [tex]\overline{a + bi} = a - bi[/tex].

    Sometimes it's used to denote equivalence classes; e.g. when it's evident you're working modulo 3, the relation [itex]2 \equiv 5 \pmod 3[/itex] can be expressed as [itex]\bar{2} = \bar{5}[/itex].
     
  4. Jun 29, 2008 #3

    matt grime

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    If you want fixed width fonts, then you need to put in some tags. I think it might be 'code'. Otherwise attempting justification doesn't work since it is font specific, or machine dependent.

    Code (Text):

      _
      z
     
     
  5. Jun 29, 2008 #4
    [tex]\overline{z}[/tex]
     
  6. Jun 29, 2008 #5
    it says the absolute value of z equals the absolute value of [tex]\overline{z}[/tex]. This was in a list of properties of absolute value.
     
  7. Jun 29, 2008 #6

    HallsofIvy

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    Okay, then you are talking about complex numbers and the "overline" denotes the complex conjugate

    If z is a complex number, say z= a+ bi, so its absolute value is [itex]|z|= \sqrt{a^2+ b^2}[/itex]. As Hurkyl said, then, [itex]\overline{z}= a- bi[/itex] so that its absolute value is [itex]|\overline{z}|= \sqrt{a^2+ (-b)^2}= \sqrt{a^2+ b^2}= |z|[/itex].

    One can also define absolute value of a complex number by [itex]|z|= \sqrt{z\overline{z}}[/itex].
     
    Last edited: Jun 29, 2008
  8. Jun 29, 2008 #7
    Thx a lot. Makes sense now.
     
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