Complex Conjugate Coordinates/Examples/2x - 3y = 5

Example of Complex Conjugate Coordinates
The equation of the straight line in the plane:
 * $2 x - 3 y = 5$

can be expressed in complex conjugate coordinates as:
 * $\paren {2 i - 3} z + \paren {2 i + 3} \overline z = 10 i$

Proof
We have that:

and so:

Hence: