Equation of a vertical line in the complex plane

[zeebo17]

Homework Statement

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

Homework Equations

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 $$z=x+i(mx+b)$$ where m is the slope of the line and b is the y-intercept, however in this case the y is undefined.

 

[Mark44]

Homework Statement

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

Homework Equations

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 $$z=x+i(mx+b)$$ where m is the slope of the line and b is the y-intercept, however in this case the y is undefined.

The y-values aren't undefined; they're arbitrary. Wouldn't your equation be z = 1 + iy, 0 <= y <= 2i?

 

[zeebo17]

Oh! Great, thanks!