Equation for Line through Two Points in Complex Plane/Parametric Form 2

Theorem
Let $z_1, z_2 \in \C$ be complex numbers.

Let $L$ be a straight line through $z_1$ and $z_2$ in the complex plane.

$L$ can be expressed by the equations:

These are the parametric equations of $L$, where $t$ is the parameter.

Proof
From Equation for Line through Two Points in Complex Plane: Parametric Form 1:


 * $z = z_1 + t \paren {z_2 - z_1}$

Letting:

the parametric equations follow by equating real parts and imaginary parts.