# Straight lines and complex numbers

1. Jan 21, 2008

### saiaspire

can anyone give me a detailed explanation on how to derive equation for a straight line, which is made up of points, each point representing a complex number..//

pls help

2. Jan 21, 2008

### Rainbow Child

To define a line you only need two points. Let them be $$z_1=x_1+i\,y_1,\,z_2=x_2+i\,y_2$$. That means that the coordinates of the two points are $$(x_1,y_1),\,(x_2,y_2)$$

• If $x_1=x_2$ then the line is $y=x_1$
• If $$x_1\neq x_2$$ then the line is of the form $$y=\lambda\,x+\kappa$$ where

$$\lambda=\frac{y_1-y_2}{x_1-x_2}$$​

and $\kappa$ can be found by demanding the line to pass through $z_1$
$$y_1=\lambda\,x_1+\kappa\Rightarrow \kappa=y_1-\lambda\,x_1$$​

3. Jan 22, 2008

### saiaspire

thanks rainbow kid