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Homework Help: Equation of a vertical line in the complex plane

  1. Feb 15, 2010 #1
    1. The problem statement, all variables and given/known data

    I need to solve [tex]\int_L \bar{z}-1[/tex] where L is the line from 1 to 1+2i.

    2. Relevant equations

    3. The attempt at a solution

    I know that I need to set z equal to the equation of the line and then integrate, but in this case I'm not sure how to express the equation of the vertical line in the complex plane.

    In the case of the non-vertical line I would write [tex] z=x+i(mx+b) [/tex] where m is the slope of the line and b is the y-intercept, however in this case the y is undefined.
  2. jcsd
  3. Feb 15, 2010 #2


    Staff: Mentor

    The y-values aren't undefined; they're arbitrary. Wouldn't your equation be z = 1 + iy, 0 <= y <= 2i?
  4. Feb 15, 2010 #3
    Oh! Great, thanks!
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