I'm working on the following exercise 2A of Jones, Gareth A., and David Singerman. Complex functions: an algebraic and geometric viewpoint. Cambridge university press, 1987.;
My attempt
A Möbius transformation preserves the Cross-ratio, we can have the following;
$$
\frac{(x_1 - z_0)(z_3 - z_2)}{(z_2 - z_0)(z_3 - z_1)} = \frac{(-1 -1)(-k-k)}{(k-1)(-k -(-1))}
$$
then I solve it w.r.t k, which leads to ugly-looking fraction....
Am I in the right direction?