Consider a bilinear transformation in the complex plane defined by \(w = \frac{(az + b) }{ (cz + d)}\) where z and w are complex variables and a, b, c, d are complex coefficients. If the transformation maps a specific circle in the z-plane into a straight line in the w-plane, what condition must hold true for coefficients a, b, c, and d?
1
a = -d and b = -c
2
a = d and b = c
3
a = b = c = d
4
a = -c and b = -d