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What is the arg() function?

  1. Apr 5, 2005 #1
    What is the arg() function? I can find no reference to it?

    exp(z)=w => z=ln(|w|)+i*arg(w)+2*k*Pi*i

    what's that arg()?
     
  2. jcsd
  3. Apr 5, 2005 #2

    dextercioby

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    A complex # is characterized through modulus & argument.

    [tex] z=\left|z\right| e^{i\varphi} [/tex]

    That [itex]\varphi [/itex] is called argument.

    The same real number appears as the argument (sic!) of the "sine" & "cosine",if u use Euler's formula in the exponential form written above.

    Daniel.
     
  4. Apr 5, 2005 #3

    dextercioby

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    And there's one more thing:

    where does that [itex] 2\pi i k,k\in \mathbb{Z} [/itex] come from...?Euler's formula explains it.It's called "multivaluedness" of the complex exponential (hence of the complex logarithm).

    Daniel.
     
  5. Apr 5, 2005 #4
    Yes, I suspected something like that yet :) but the term is described nowhere in our course. {or I still have to find it}

    Thx.
     
  6. Apr 6, 2005 #5
    So, basically, arg(z) = arccos(Re(z))?
     
  7. Apr 6, 2005 #6

    dextercioby

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    Well,arccos returns a value in the interval [itex] [0,\pi] [/itex],while that argument can be any #,complex even...

    Daniel.
     
  8. Apr 6, 2005 #7

    Zurtex

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    I don't see how that works, you saying that:

    arg(70) = arg(109i + 70)?

    Shouldn't there be something else in there?
     
  9. Apr 6, 2005 #8

    dextercioby

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    No,he's saying something like

    [tex] \arg (70+3i)=\arccos 70 [/tex]

    which is ballooney.

    Daniel.
     
  10. Apr 6, 2005 #9
    No. You can write

    [tex]\arg z = \arccos \left( \mbox{Re}\left[ \frac{z}{|z|} \right] \right)[/tex]

    in a form similar to yours. The standard definition is if [itex]z = x + iy[/itex] then

    [tex]\arg z = \arctan \left(\frac{y}{x}\right)[/tex]

    though.
     
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