Transformations on the complex plane

Question

I'm trying to work out what the transformation $T:z \rightarrow -\frac{1}{z}$ does (eg reflection in a line, rotation around a point etc). Any help on how to do this would be greatly appreciated! I've tried seeing what it does to $1$ and $i$ but is hasn't helped me. Thanks!

Answer 1

What does negation do? Then what does taking the reciprocal do to the length and the angle? Note that you will need to know what inversion is, to describe what happens to the length.

Answer 2

It's a circle inversion, followed by a reflection over the y axis.