Interpretación geométrica de la ecuación del círculo en el plano complejo usando la función de valor real equivalente

A function of a circle in the complex plane is obtained. The complex function represents the complex roots (discriminant less than zero) and the unique real solution (discriminant is equal to zero) of the first (or second) tangent circles to the real-valued function that represents the superior (or inferior) part of a circle with center on the -axis. In other words, if tangent circles are drawn to a circle with center on the -axis, the roots of the tangent circles that do not touch the -axis and the root of the tangent circle that only touch the -axis at one point are located on a circle in the complex plane.A function of a circle in the complex plane is obtained. The complex function represents the complex roots (discriminant less than zero) and the unique real solution (discriminant is equal to zero) of the first (or second) tangent circles to the real-valued function that represents the superior (or inferior) part of a circle with center on the -axis. In other words, if tangent circles are drawn to a circle with center on the -axis, the roots of the tangent circles that do not touch the -axis and the root of the tangent circle that only touch the -axis at one point are located on a circle in the complex plane