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Math Help - complex: question about transformations

  1. #1
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    complex: question about transformations

    1. Prove that the most general transformation which leaves the origin fixed and preseerves all distances is either a rotation or a rotation followd by reflexion in the real axis.

    2. Show that any four distinct points can be carried by a linear transformation to position 1, -1, k, -k, where the value of k depends on the points. How many solutions are there, and how are they related?

    Please help me to solve these problems. Thanks!
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  2. #2
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    Quote Originally Posted by conmeo View Post
    1. Prove that the most general transformation which leaves the origin fixed and preseerves all distances is either a rotation or a rotation followd by reflexion in the real axis.

    2. Show that any four distinct points can be carried by a linear transformation to position 1, -1, k, -k, where the value of k depends on the points. How many solutions are there, and how are they related?

    Please help me to solve these problems. Thanks!
    In what space are you working? I would think \mathbb{C} but then 2 is obviously false: 1,2,3,4
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