# Math Help - Rotation of the Riemann Sphere

1. ## 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).

2. Originally Posted by srw899
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.

3. ## 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.