How to write the equation of a line in $\mathbb C^n$? I want to write the equation of a line in $\mathbb C^n$ passing through a point $(z_1,z_2,...,z_n)$. Actually I have a set of points and I suspect they all lie on the same line which passes through this point and I want a convenient way to check it.
Thank you

It doesn't matter if you work with complex, real numbers, or elements of any field $\mathbb{K}$: if you have a point $p = (z_1, \dots , z_n) \in \mathbb{K}^n$, or any $\mathbb{K}$-vector space $V$, an equation for a straight line in $\mathbb{K}^n$ (or in $V$) passing through $p$ may always be written, for instance, as
$$
p + \lambda v \ ,
$$
with $v= (v_1, \dots , v_n) \in \mathbb{K}^n$ (or $v\in V$) and $\lambda \in \mathbb{K}$.
