You can find if two rea-valued vectors $x$ and $y$ in $\Re^n$ are colinear by calculating.
$\cos(\theta) = \frac{\langle x, y \rangle}{\lvert x\rvert\,\lvert y\rvert} $
For complex vectors ($z \in C^n$), this definition doesn't work. In this post, they comment on hyperbolic geometry and how to find the angle between two vectors. Why do we use cosh to define the angle between two vectors in hyperbolic geometry?
However, what would this hyperbolic angle mean in terms of colinearity?