Complex function representing rotation of the plane

Question

The function $f(z) = \dfrac{(-1 + i \sqrt{3}) z + (-2 \sqrt{3} - 18i)}{2}$ represents a rotation around some complex number $c$. Find $c$.

I'm not even sure what this question means. I need help.

Answer 1

When a plane is rotated about some point, that point remains in place (does not move), as it's the center of rotation.

The fact of not moving (being a fixed point) is expressed by the equation $f(z)=z$. Solve it, and you are done.