Direction of line parallel to the x-axis in the complex plane

Question

How can say the direction of a line parallel to the real axis as clockwise or anti-clockwise?

More precisely what's the direction of blue line as well as orange line ?

Which one is clockwise & which one is anti-clockwise ?

Update :

My actual question is : Suppose this is the whole contour where I want to integrate a complex function. The middle line is the negative real axis. For part $C_2$ the direction is anticlockwise (positively oriented). But for the curve $C_1$ and $C_3$ the direction is clockwise or anticlockwise so that I can use negative sign and positive sign in the evaluation of the integration on the whole contour ? How can I say that ?

Answer 1

A line doesn't have a direction. It has an equation.

A vector has origin and direction.

The lines above would have equations of the form Im(z) = c for some real c.

As vectors, their specification would be a+bt where $t \ge 0$ and b is real.

If b > 0, the vector goes to the right.

If b < 0, the vector goes to the left.

Answer 2

I'd avoid using the terms "clockwise" or "anti-clockwise" since they don't apply in this context. These only refer to things moving in a circular way.

I would agree with marty cohen: we would say that these lines "go to the right/left", or "the direction of the line is to the right/left".

P.S. This question might be better off on english.stackexchange.com