# Angles in the Complex Plane

See pic

Hello,

I've been doing some work on Complex Numbers. In the description of the picture I attached above, it states "|z_2 - z_1 | = AB, and arg(z_2-z_1) is the angle between the vector AB and the positive direction of the x-axis"

I don't seem to understand where the angle between vector AB and the positive direction of the x-axis would be. For example, for a vector OP, where O is the origin, I know that the argument would be between OP and the positive x-axis. But I cannot seem to visualise where the argument for AB would be.

I hope someone can make sense of what I'm asking, thanks in advance.

The argument for $AB$ is the same as the argument for $OC$. It doesn't matter where exactly in the plane your vector is sitting. All that matters is its direction and length. You may translate a vector (without rotating or scaling it) however you want, and it is the same vector.
So, to visualize the argument of $AB$, just imagine first shifting it so that it begins at the origin.