Prove that the stereographic projection z of the point (0, d) (in spherical polar coordinates) on...

 

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Prove that the stereographic projection z of the point (0, d) (in spherical polar coordinates) on the Riemann sphere is given by z = cot (4/2) eie. Hence prove that the mapping f(z) = 1/z on C induces a rotation of the Riemann sphere about the real axis, through an angle . Prove that the stereographic projection z of the point (0, d) (in spherical polar coordinates) on the Riemann sphere is given by z = cot (4/2) eie. Hence prove that the mapping f(z) = 1/z on C induces a rotation of the Riemann sphere about the real axis, through an angle .

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