Results 1 to 2 of 2

Math Help - Complex Mapping

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    3

    Complex Mapping

    Find the image of the following region:




    under the action of
    f(z)=e^{\bar{z}}
    (e raised to z conjugate)


    I am lost on this one. Thanks for any advice with this one.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by hilbertcube182 View Post
    Find the image of the following region:




    under the action of
    f(z)=e^{\bar{z}}
    (e raised to z conjugate)


    I am lost on this one. Thanks for any advice with this one.
    Let \psi be the angle y=\tfrac{x}{2} makes and \phi be the angle y=3x makes.

    Your region can be described as, \{ re^{i\theta} | r \in \mathbb{R}^{\times}, \psi <\theta < \phi \}.

    This means, f(re^{i\theta}) = \exp ( \overline{re^{i\theta}} ) = \exp ( r e^{-i\theta}) = e^{r\cos\theta}e^{-ir\sin \theta}.

    Now r\cos \theta,r\sin\theta ranges through all values of \mathbb{R}^{\times}. Therefore, the range is r'e^{i\theta'} where \theta'\in \mathbb{R}^{\times} and r'>0,r'\not = 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex open mapping & conformal mapping problems.
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 22nd 2011, 07:26 AM
  2. Mapping of complex numbers
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 1st 2010, 08:20 PM
  3. Complex Mapping
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: June 18th 2010, 09:34 AM
  4. Complex Mapping
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 6th 2009, 04:11 PM
  5. complex mapping
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 1st 2008, 07:17 PM

Search Tags


/mathhelpforum @mathhelpforum