Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Complex Analysis Mobius Transformations
Consider a Mobius transformation \(T(z) = \frac{az + b}{cz + d}\) where a = 1, b = i, c = 1, and d = -i. Which of the following is a true statement regarding this transformation?
1
T maps the real axis onto itself.
2
T has exactly one fixed point on the unit circle.
3
T preserves the cross-ratio of any four points in the complex plane.
4
The transformation T is its own inverse.
5
Question Not Attempted