Although the question does not explicitly say so, it is usually assumed that hyperbolic space consists of the upper half of the complex plane. So in this problem I think it's safe to ignore the lower half of the plane.

To calculate

, you have to take the real part of z and the imaginary part of z, square them both, and then add. If

(where a and b are both real) then

. The real part is

and the imaginary part is b. So

.

Good grief, I think you're right.

This is very advanced material, and it looks as though this course assumes a lot of previous experience of working with complex numbers and their geometry.