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Complex variables- graphing an equation

  1. Sep 13, 2011 #1
    1. The problem statement, all variables and given/known data

    Suppose that c is a member of the Real numbers, and p is a member of the Complex numbers with p not equal to 0, are given numbers.

    (a) Show that pz + conjugate(pz) + c = 0 is the equation of a straight line in the plane.

    Provide a carefully-drawn plot that illustrates your solution for a few given values of the constants c and p .

    2. Relevant equations

    z is a complex number (i.e. x+iy)

    3. The attempt at a solution

    a) After simplifying the conjugates: px +ipy + px - ipy + c = 0
    After collecting like terms: 2px + c = 0
    Solving for x: x = -0.5(c/p)

    Now, I don't understand how the graph would look like. Would it be a vertical line on the real vs imaginary axes?

    Thank you.
  2. jcsd
  3. Sep 13, 2011 #2
    Looks like it to me.
  4. Sep 13, 2011 #3

    Ray Vickson

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    I thought you said that p was a complex number; it does not appear so in what you have done.

  5. Sep 13, 2011 #4
    p is a constant that is a member of the set of complex numbers. Does that make sense?
  6. Sep 15, 2011 #5
    I see what you mean now, Ray. I think I got it now!
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