Equation for Line through Two Points in Complex Plane/Examples/2+i, 3-2i/Parametric Form 1

Example of Use of Equation for Line through Two Points in Complex Plane
Let $L$ be a straight line through $2 + i$ and $3 - 2 i$ in the complex plane.

Then $L$ can be expressed by the equation:
 * $z - \paren {2 + i} = t \paren {1 - 3 i}$

Proof
From Equation for Line through Two Points in Complex Plane: Parametric Form $1$, a straight line $L$ passing through $2$ points $z_1$ and $z_2$ has the equation:


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

Hence: