Results 1 to 2 of 2

Math Help - Mapping of complex numbers

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    41

    Mapping of complex numbers

    Hi, I'm not sure of the answer to this question (or even if belongs in this forum, apologies):

    Let ϕ: C → C be the rotation of angle θ around the point z_0 ∈ C.
    Express ϕ(z ) in terms of z , z_0 and e^iθ.

    I know that z = (r, θ) in polar coordinates means z=re^iθ , but I don't know how to express ϕ(z). My best guess is ϕ(z) = z_0e^iθ but I don't really understand how to visualize this rotation or where z is.

    Thanks so much for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Failure's Avatar
    Joined
    Jul 2009
    From
    Zürich
    Posts
    555
    Quote Originally Posted by kimberu View Post
    Hi, I'm not sure of the answer to this question (or even if belongs in this forum, apologies):

    Let ϕ: C → C be the rotation of angle θ around the point z_0 ∈ C.
    Express ϕ(z ) in terms of z , z_0 and e^iθ.

    I know that z = (r, θ) in polar coordinates means z=re^iθ , but I don't know how to express ϕ(z). My best guess is ϕ(z) = z_0e^iθ but I don't really understand how to visualize this rotation or where z is.
    Do it in three steps: first, translate the plane so that z_0 comes to lie at the origin, 0. Second, rotate the plane around the origin by \theta, and finally shift the origin back to z_0.
    So the first step is z\mapsto z-z_0, combined with the second, you have z\mapsto (z-z_0)e^{i\theta}, and combined with the third, you get z\mapsto \phi(z) := (z-z_0)e^{i\theta}+z_0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mapping complex numbers
    Posted in the Differential Geometry Forum
    Replies: 8
    Last Post: March 16th 2011, 05:04 AM
  2. Complex open mapping & conformal mapping problems.
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 22nd 2011, 07:26 AM
  3. Complex Mapping
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 6th 2009, 04:11 PM
  4. Complex Numbers Mapping (DUE TOMORROW)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 30th 2008, 05:36 PM
  5. Replies: 1
    Last Post: May 24th 2007, 03:49 AM

Search Tags


/mathhelpforum @mathhelpforum