What is the equation of a straight line in the complex plane? There are many different forms, but I want to look at some of the simplest ones.
If you know the slope $m \in \mathbb{R}$ and intercept $b \in \mathbb{R}$ of the line, you can write an equation in parametric form $$ z = x + i (m x + b) ,$$ where $x \in \mathbb{R}$ and $z \in \mathbb{C}$.