Straight lines and complex numbers

[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

 

[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 $z_1$
  
  $$y_1=\lambda\,x_1+\kappa\Rightarrow \kappa=y_1-\lambda\,x_1$$​

 

[saiaspire]

thanks rainbow kid