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Derivation of mapping for isometric rotation about i

  1. Nov 15, 2014 #1
    1. The problem statement, all variables and given/known data
    2. Find the formulae as in (3.4.1) for each of the following:
    (a) the rotation of angle π/2 about the point i ;

    2. Relevant equations
    The equation 3.4.1 is given below.
    ## f(z) → z*a + b ##
    where a, b and z are all complex numbers


    3. The attempt at a solution
    I have attached my attempt at the solution but my solution is wrong!!
     

    Attached Files:

  2. jcsd
  3. Nov 15, 2014 #2

    Dick

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    You want to start out with ##\left( z-w \right) e^{i \theta}##. No absolute value! Now just put in what ##w## and ##\theta## are.
     
  4. Nov 16, 2014 #3
    Thanks Dick!!

    I tried the problem and the solution is as attached
     

    Attached Files:

  5. Nov 16, 2014 #4

    Dick

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    I'm not sure what part of that is supposed to be the answer. The answer is ##f(z)=\left( z-w \right) e^{i \theta}+w##. You seem to know ##w=i## and ##e^{i \pi/2}=i##. Just put those values in! Then try to express it in the form ##f(z)=az+b##.
     
    Last edited: Nov 16, 2014
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