Hi, I'm not sure of the answer to this question (or even if belongs in this forum, apologies):

Let ϕ: C → C be the rotation of angle θ around the point $\displaystyle z_0$ ∈ C.

Express ϕ(z ) in terms of z , $\displaystyle z_0$ and e^iθ.

I know that z = (r, θ) in polar coordinates means z=re^iθ , but I don't know how to express ϕ(z). My best guess is ϕ(z) = $\displaystyle z_0$e^iθ but I don't really understand how to visualize this rotation or where z is.

Thanks so much for any help.