Educação Superior::Ciências Exatas e da Terra::MatemáticaThe points {z,w} belong to C² of the complex unit circle z² + w² =1 can be parametrized: z = x + iy = cos(α)cosh(β) - isin(α)sinh(β), w = u + iv = sin(α)cosh(β) + icos(α)sinh(β). This Demonstration shows 3D projections of the surface z² + w² = 1 in x, y, u, v space. The angles φ_(a,b) denote the rotation angles inside the a, b hyperplane. In the limit, as β -> 0, the complex unit circle becomes a circle in the x, u plane