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

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:
 * $3 x + y = 7$

Proof
From Equation of Straight Line in Plane: Two-Point Form, a straight line $L$ passing through $2$ points $z_1 = x_1 + i y_1$ and $z_2 = x_2 + i y_2$ has the equation:


 * $\dfrac {x - x_1} {x_2 - x_1} = \dfrac {y - y_1} {y_2 - y_1}$

Hence: