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Straight lines and complex numbers

  1. Jan 21, 2008 #1
    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. jcsd
  3. Jan 21, 2008 #2
    To define a line you only need two points. Let them be [tex]z_1=x_1+i\,y_1,\,z_2=x_2+i\,y_2[/tex]. That means that the coordinates of the two points are [tex](x_1,y_1),\,(x_2,y_2)[/tex]

    • If [itex]x_1=x_2[/itex] then the line is [itex]y=x_1[/itex]
    • If [tex]x_1\neq x_2[/tex] then the line is of the form [tex]y=\lambda\,x+\kappa[/tex] where

      [tex]\lambda=\frac{y_1-y_2}{x_1-x_2}[/tex]​

      and [itex]\kappa[/itex] can be found by demanding the line to pass through [itex]z_1[/itex]
      [tex]y_1=\lambda\,x_1+\kappa\Rightarrow \kappa=y_1-\lambda\,x_1[/tex]​
     
  4. Jan 22, 2008 #3
    thanks rainbow kid
     
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