Argand diagram problem

Question

Why is the point P is removed? Please help.

Answer 1

The point $P=2i$ is removed because if you plug it in to the function $z-2i$ you get $0$, which doesn't have an argument.

Answer 2

Well, if you relate complex numbers to vectors, substituting for $P$ in the $\arg ()$ we get $0$ or a null vector. Since a null vector does not have any direction, its argument is not defined.