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Elementary Functions > ArcTan[z] > Visualizations

Riemann surfaces

Real and imaginary parts of the continuation of over the . The real part is a faithful representation of the Riemann surface of .

Real part of the continuation of over the . The logarithmic branch point at is clearly visible. The viewpoint is from the lower half‐plane.

Real parts of the continuation of over the Riemann sphere. The branch points are at the intersection of the equator with the ‐plane