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Homework Help: Argand Diagram: Difference in argument = pi/4

  1. Jun 4, 2013 #1
    1. The problem statement, all variables and given/known data

    Sketch the locus of points in the argand diagram defined by z:

    arg (z-1) - arg(z+1) = ∏/4

    2. Relevant equations

    3. The attempt at a solution

    By simple geometry i worked out that at a point in the x-y plane, the angle subtended from that point to -1 and 1 must be = pi/4.

    For a circle I know this must be = pi/2. But for pi/4 I have no clue..
  2. jcsd
  3. Jun 4, 2013 #2


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    If ##z=x+yi## and you call ##\theta_1=arg(z-1)##and ##\theta_2=arg(z+1)## what happens if you calculate ##\tan(\theta_1-\theta_2)##?
  4. Jun 4, 2013 #3


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    I know that it's a different circle, but that's for me you know and you to find out after you put some work in on this. How do you know pi/2 defines a circle? Apply the same ideas.
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