To derive this equation, we use what we know about perpendicular circles. Any Poincaré line, as part of a Möbius circle, has an equation of the form for some complex and real with . The edge circle has equation , so the first circle is perpendicular to the edge whenever , i.e., whenever . The equation becomes and the condition on the coefficients becomes . We may assume that is non-negative (mulitply the equation through by if necessary), so if we take square roots, the condition becomes .