What is the image of the region ∣z∣<1|z| < 1∣z∣<1 under the mapping f(z)=z−1z+1f(z) = \frac{z-1}{z+1}f(z)=z+1z−1?
Left half-plane Re(w)<0\text{Re}(w) < 0Re(w)<0
Right half-plane Re(w)>0\text{Re}(w) > 0Re(w)>0
Unit disk ∣w∣<1|w| < 1∣w∣<1
Upper half-plane