# math

## Lines in the Complex Plane

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 $$z \in \mathbb{C}$$.