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