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Math Help - Complex analysis, find the image of a transformation

  1. #1
    MHF Contributor arbolis's Avatar
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    Complex analysis, find the image of a transformation

    Find the image of the region 0<x<1 under the transformation T: z \to iz.
    Attempt: I write z=a+ib where 0<a<1 and b can be any real number. So the transformation takes these z and output i(a+ib)=-b+ia.
    On the complex plane that makes an infinite horizontal region bounded above by i and below by 0?
    While the original graph would be an infinite vertical region bounded on the right by 1 and on the left by 0.
    Am I right? I'm quite rusty, I'm trying to end my vacations by starting maths back.
    Thanks for any insight.
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  2. #2
    A Plied Mathematician
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    Sounds right to me. Multiplication by i is a counter-clockwise rotation by \pi/2, if that helps your understanding.
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  3. #3
    MHF Contributor arbolis's Avatar
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    Ok thank you. You're right, I had "forgotten" that a multiplication by i has a rotation effect.
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