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Images of concentric circles around the origin Images of concentric circles of radii between  and  around the origin under the (conformal) map  . All circles are mapped into the right half‐plane. Images of the Riemann sphere of concentric circles of radii between  and  around the origin under the (conformal) map  . Circles are split because of the branch cut along the imaginary axis. Images in the  ‐plane of concentric circles of radii between  and  around the origin under the (conformal) map  . Images of radial rays originating from the origin Images of rays from the origin under the (conformal) map  . Images on the Riemann sphere of rays from the origin under the (conformal) map  . Images of a square grid Images of a square grid of size  under the (conformal) map  . Images of the tessellated Riemann sphere Images of triangles on the Riemann sphere under the (conformal) map  . Plane to plane map Curves  parametrized by  . Points  (where  ) move smoothly into points  .
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