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Mobius tranformation

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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.

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