Which condition on zzz ensures that z−1z+1\frac{z-1}{z+1}z+1z−1 is purely imaginary?
∣z∣=1|z|=1∣z∣=1
zzz is real
∣z∣=0|z|=0∣z∣=0
arg(z)=0\text{arg}(z)=0arg(z)=0