Let T be a M¨obius transformation such that T(0) = α, T(α) = 0 and T(∞) = −α, where α = (−1 + i)/ √2. Let L denote the straight line passing through the origin with slope −1, and let C denote the circle of unit radius centred at the origin. Then, which of the following statements are TRUE?
1
T maps L to a straight line
2
T maps L to a circle
3
T−1 maps C to a straight line
4
T−1 maps C to a circle