Consider you are given a bilinear transformation of the form \(w = \frac{(az + b)} { (cz + d)}\) , where a, b, c, and d are fixed complex numbers, and there is a condition that (ad - bc) ≠ 0. Which of the following statements is correct?
1
Any two distinct points of the z-plane can be brought to coincide in the w-plane using this transformation.
2
Any three points on the z-plane can be mapped onto any three points in the w-plane.
3
This transformation can convert an arbitrary ellipse in the z-plane to a circle in the w-plane.
4
This transformation can turn the entire z-plane into a single point in the w-plane.