1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex analysis - graphing in complex plane

  1. Sep 20, 2009 #1
    1. The problem statement, all variables and given/known data
    Graph the following in the complex plane
    {zϵC: (6+i)z + (6-i)zbar + 5 = 0}

    2. Relevant equations


    3. The attempt at a solution

    Substituting the equations gives
    2(6x-y) + 5 = 0
    => y = 6x + (5/2)

    But that's a line in R^2. The imaginary parts canceled. The question asks to graph it in the complex plane. So what will it look like?
  2. jcsd
  3. Sep 20, 2009 #2
    I was told that it was all complex numbers of form x + (6x + 5/2)i but i don't understand how that's derived since I got only a line in R^2
  4. Sep 20, 2009 #3
    Identify x+iy with the point (x,y) in the plane.

    x+iy = (x,y)

    Your answer is the same as the suggested answer. You found {(x,y) : y=6x +5/2}. The suggested answer is the same thing:
    {x+iy : y=6x + 5/2}, i.e. {x + i(6x+5/2) : x is real}
  5. Sep 20, 2009 #4
    Thanks, I get the part about substituting x for y. But what does that look like in the complex plane in terms of where it crosses the real and imaginary axes?
  6. Sep 20, 2009 #5
    It's the line y=6x+5/2, just like in elementary algebra. The real axis is the x-axis, and the imaginary axis is the y-axis.
  7. Sep 20, 2009 #6
    but then isn't it an Argand diagram with coordinate axes of y and x. isn't that somewhat different than if the coordinate axes were Im and Re? (it is just somewhat confusing since in graphing it like in elementary algebra, the i is implicit otherwise it is as if it's in R^2 !!! strange...)
    Last edited: Sep 20, 2009
  8. Sep 20, 2009 #7
    No difference. That's what graphing in the complex plane means.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Complex analysis - graphing in complex plane
  1. Complex Analysis (Replies: 4)

  2. Complex Analysis (Replies: 4)

  3. Complex analysis (Replies: 10)