Consider a bilinear transformation of the complex variable z given by \(w = \frac{(az + b)} { (cz + d)}, \) where a, b, c, and d are complex numbers. If a = 1, b = 2, c = -3, and d = 4, then which of the following statements is true?
1
The transformation rotates and scales the complex plane, but does not translate it.
2
The transformation maps every line or circle in the z-plane to a line or circle in the w-plane.
3
The transformation only applies to the right half of the complex plane.
4
The transformation cannot change the shape of any region in the z-plane.
5
Question Not Attempted