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!

Z-plane to w-plane mapping

  1. Oct 30, 2011 #1
    1. The problem statement, all variables and given/known data
    Consider the mapping w = 1/(z-1) from the z-plane to the w plane. Show that in the z plane the circle
    (x-2)² + y² = 4
    maps to a circle in the w-plane. What is the radius of this circle and where is it's centre.

    So in the z-plane this is a circle with radius 2 at the point (1,0) in the z plane.

    2. Relevant equations



    3. The attempt at a solution
    Hmmm. Well I know that w = 1/(z-1) => u² + v² = 1 / ((x-1)² +y²)

    I presume that will help at some point

    In the z-plane (x-1)² + y² = 4 what part is the imaginary part? The z plane has 2 axes:
    x and y... am I right in thinking x = Re and y = Im? I recall f(z) = u(x,y) + iv(x,y) but does that mean u = (x-1)² + y² ??? How does the 4 come into it. What about the imaginary part?

    I think I may of bodged it by getting

    (x-1)² + y² = (1/2)^2

    by sticking 1 / ((x-1)² +y²) = 4, but I don't think that is the correct method.

    Thanks
    Thomas
     
  2. jcsd
  3. Oct 30, 2011 #2

    Mark44

    Staff: Mentor

    The center of the circle would be at (2, 0), not (1, 0).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Z-plane to w-plane mapping
  1. Spheres and planes (Replies: 7)

  2. Rotation on a plane (Replies: 3)

Loading...