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Complex analysis

  1. Oct 6, 2006 #1
    Hello everyone,

    I am trying to solve this follow problem, but don't quite know how to go about getting Arg(z).

    z = 6 / (1 + 4i)

    I got that lzl is sqrt((6/17)^2+(-24/17)^2) but am stuck with finding Arg(z). It told me to recall that -pi < Arg(z) <= pi

    Can you guys teach me how to go about finding arrrggg... this Arg(z)?

    TIA.
     
  2. jcsd
  3. Oct 6, 2006 #2

    Hurkyl

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    Is there any sort of number for which you know how to compute Arg?
     
  4. Oct 6, 2006 #3
    This Arg(z) thing is new to me, so no. I'm trying to find out what it is. Thanks.
     
  5. Oct 6, 2006 #4
    I found this on Google:

    The argument of a complex number is the angle between the positive x-axis and the line representing the complex number on an Argand diagram. It is denoted arg (z)

    So Arg(z) is pretty much just the angle theta that r makes with the x-axis?

    Assuming that arg(z) is not case sensitive, then is it simply arctan(-4) in this case?
     
    Last edited: Oct 6, 2006
  6. Oct 6, 2006 #5

    Hurkyl

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    In this case, yes, Arg(z) = Arctan(-4). (but be wary; for some z, Arg(z) cannot equal the Arctangent of anything at all! You have to make sure you take the right value for the arctangent)

    Arg/arg is case sensitive, just like other complex functions. arg is a "multi-valued function", whereas Arg picks out a specific value.
     
    Last edited: Oct 6, 2006
  7. Oct 6, 2006 #6
    Thank you so much Hurkyl... your help is much appreciated! In the meantime, I also found this page, which led me to believe that I was right. Your reply, however, gave a positive confirmation of my guess. Thanks again - now I have a much better grasp of this concept.

    Yang
     
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