Complex Circle, 1 Slit Framed & Mounted Print

The equation \(x^2 + y^2 = 1\) describes the unit circle in the real Cartesian plane. We may write \(y = \pm\sqrt{1 - x^2}\) and treat the circle as a union of two semi-circle graphs.

Similarly, the equation \(z^2 + w^2 = 1\) in the complex Cartesian plane describes a surface that can be written as a union of two graphs. The complex square root is only continuous if we remove branch cuts, and the two graphs here are only continuous if we slit the complex plane somewhere.

This image shows continuous branches, one green, the other blue, on the plane with the real interval \([-1, 1]\) removed.

Created from high-quality wood, milled with simple clean lines and presented with a satin finish. Includes an off-white mount that will not discolour or fade with age. - Simple, elegant design - Premium, fine art paper with a gently textured surface - Handmade by specialist picture framers - FSC certified off-white mat / window mount - Delivered ready for hanging