Equation for Line through Two Points in Complex Plane/Formulation 1

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 equation:
 * $\map \arg {\dfrac {z - z_1} {z_2 - z_1} } = 0$

Proof
Let $z$ be a point on the $L$.

Then:
 * $z - z_1 = b \paren {z - z_2}$

where $b$ is some real number.

Then: