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Complex Variables - Mappings

  1. Feb 11, 2012 #1
    Complex Variables - Mappings under e^z

    1. The problem statement, all variables and given/known data
    Find the image of S1,S2 under ez.
    S1 = {z=x+iy : 0 < y < [itex]\pi[/itex] }
    S2 = {z=x+iy : x > 0, 0 < y < [itex]\pi[/itex] }



    2. Relevant equations
    w=ez
    w=[itex]\rho[/itex]ei[itex]\varphi[/itex]
    [itex]\rho[/itex]=ex, [itex]\varphi[/itex]=y

    3. The attempt at a solution
    Did not know how to get started. I don't know how to use the above equations to help me. Thank you very very much!
     
    Last edited: Feb 11, 2012
  2. jcsd
  3. Feb 11, 2012 #2

    SammyS

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    Re: Complex Variables - Mappings under e^z

    You might start by identifying what the set, S1 and S2 are.
     
  4. Feb 12, 2012 #3
    The answer the professor has is {ω= u + iv : v > 0}.

    I really do not understand how to use the equations and arrive here. I HAVE to be missing something simple. I really appreciate any help that can push me into the right direction
     
  5. Feb 12, 2012 #4

    SammyS

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    So, do you know what the sets S1 and S2 look like on the complex plane ?

    (I tried to push you this way earlier.)
     
  6. Feb 12, 2012 #5
    I do not know what it looks like in the complex plane. What can I do to help me visualize it?
    I really appreciate the help
     
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