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Math Help - Mobius Transformations

  1. #1
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    Mobius Transformations

    Unsure if this is the right section but here goes:

    By coordinte geometry, any line or circle is of the form Ax+By+C( x^2 + y^2) = D, where A, B, C, D are real constants.

    Set \frac{1}{z} = u + iv.

    Show that u = \frac{x}{x^2 + y^2} and v = \frac{-y}{x^2 + y^2}.

    Deduce that the linear fractional transformation sends a line or a circle to another such.

    I'm really quite stumped by this...I don't see where the 1/z comes into all this...and just in general don't know how to start with this?

    Any hints or help would be greatly appreciated.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by scorpio1 View Post
    Unsure if this is the right section but here goes:

    By coordinte geometry, any line or circle is of the form Ax+By+C( x^2 + y^2) = D, where A, B, C, D are real constants.

    Set \frac{1}{z} = u + iv.

    Show that u = \frac{x}{x^2 + y^2} and v = \frac{-y}{x^2 + y^2}.

    Deduce that the linear fractional transformation sends a line or a circle to another such.

    I'm really quite stumped by this...I don't see where the 1/z comes into all this...and just in general don't know how to start with this?

    Any hints or help would be greatly appreciated.
    You are dealing with a circle (or line) in the complex plain, thus z=x+iy. now proceed.

    RonL
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