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Math Help - Rotation of the Riemann Sphere

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    Rotation of the Riemann Sphere

    the mapping w=-1/z corresponds to a 180 degree rotation of the Riemann sphere about the x2-axis (the imaginary axis).
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    Quote Originally Posted by srw899 View Post
    the mapping w=-1/z corresponds to a 180 degree rotation of the Riemann sphere about the x2-axis (the imaginary axis).
    The mapping z\mapsto -\tfrac{1}{z} can be visualized as two mappings, the first z\mapsto -z followed by z\mapsto \tfrac{1}{z}. Remember that z\mapsto -z will rotate the Riemann sphere by 180 degrees while z\to \tfrac{1}{z} will flip the Riemann sphere over upside down. Putting these effects together we get exactly what z\mapsto -\tfrac{1}{z} does.
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    another question

    show The mapping w=(e^i*theta)z corresponds to a rotation of the riemann sphere about the xyaxis through an angle theta.
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