Angle of rotation of $w = \frac{1}{z}$ at the points $1$ and $i$ What angle of rotation is produced by the transformation $w=\frac{1}{z}$ at the point
(a) $z_{0} = 1$
(b) $z_{0} = i$
I'm not sure what to do. At first I though about representing $w=\frac{1}{z}$ in polar coordinates and then plugging in the point in question, but I know this is wrong...
I also know I am supposed to do something with differentiation...do I take $zf'(z)$ or something like that and then plug in i and compare the change in angle from the point in question? I am quite confused.

Here , $f(z)=\frac{1}{z}$. $f'(z)=-\frac{1}{z^2}$.
Angle of rotation at the point $z_0=1$ is $\arg f'(1)=\arg(-1)=\pi$.
Angle of rotation at the point $z_0=i$ is $\arg f'(i)=\arg(1)=0$.
