## Upon reflection

The Riemannian spherical representation of the complex plane brings wonderful insights into complex functions. The above video illustrates *complex inversion * (as per Needham), i.e.

This can be decomposed into:

(inversion)

and

(complex conjugation)

i.e.

On the sphere, the first operation corresponds to reflection in the plane z=0 and the second operation to reflection in the plane y =0. The composition yields a rotation of 180 degrees around the x (real axis).

The cdf of the video is here.

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Categories: Mathematica, Mathematics

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