Mobius tranformation

[Nikita Dua]

What is the formula or way for finding the rotation angle (arg(𝑓′(𝑧))) for the derivative of Mobius transformation?

[Ye Jin]

For example, z=2+i, f(z)=$z^2$
f'(z)=2(2+i)
arg(f'(z))=arctan$\frac{1}{2}$
because4+2i represents the point (4,2) and the arg for (4,2) is arctan$\frac{1}{2}$
Hope it works for you.