Is $f(z) = 2z+i$ an homotetic transformation or a rotation ?
It's hard for me to see how to answer this question. Here is what I've done so far :
$f(z)$ is of the form $f(z) = k \cdot z + b$ with $k \in \mathbb{R}$ hence it's an homotetic transformation. Yet the fact that we add $b$ confuses me. Does it mean that this function is the composition of an homotetic transformation and a translation ?
Put $z'= f(z)$. Since $$z'-(-i) = 2(z-(-i))$$ it is just homothety with center at $-i$ and coefficient of similarity $k=2$.