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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  . Large circles are mapped into parallel lines with increasing real parts. Images of the Riemann sphere of concentric circles of radii between  and  around the origin under the (conformal) map  . Circles are split into two parts because of the branch cuts 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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