Why when the angle between AM and BM is k*pi then the group of points is the line (AB) - [A,B]?

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I'm sorry for my broken English(I don't know much Math vocabulary in English)

This is all on the complex plane, just to say.

My question is:

When arg(AM/BM) = k*pi

Then it means the group of points is the line (AB) except the two points A and B? I don't get it.