Results 1 to 2 of 2

Math Help - Complex Mappings

  1. #1
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Complex Mappings

    According to the Remarks in Section 2.5, since f(z)=\frac{1}{z} is its own inverse function, the mapping w=\frac{1}{z} on the extended complex plane maps the circle |z-\frac{1}{2}|=\frac{1}{2} to the line Re(w) = 1. Verify this.

    I am not sure how to do this without working backwards which isn't an easy method. Does anyone know how this can be done in a more efficient manner?

    Thank you for your time,

    Dustin.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by dwsmith View Post
    According to the Remarks in Section 2.5, since f(z)=\frac{1}{z} is its own inverse function, the mapping w=\frac{1}{z} on the extended complex plane maps the circle |z-\frac{1}{2}|=\frac{1}{2} to the line Re(w) = 1. Verify this.

    I am not sure how to do this without working backwards which isn't an easy method. Does anyone know how this can be done in a more efficient manner?

    Thank you for your time,

    Dustin.
    On the circle you may put z=\frac{1}{2}(1+e^{i\theta}), \theta \in [0,2\pi)

    Now compute w=\frac{1}{z} and show that its real part is equal to $$ 1 and its imaginary part takes every real value for some $$ \theta \in [0,2\pi)

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex Mappings
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 3rd 2010, 03:05 PM
  2. Complex analysis - mappings
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: January 24th 2010, 04:27 PM
  3. Mappings by 1/z
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 16th 2008, 12:22 PM
  4. mappings
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: August 2nd 2008, 11:20 AM
  5. Complex Analysis Question regarding mappings.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 6th 2008, 01:46 AM

Search Tags


/mathhelpforum @mathhelpforum