Question about system stability

[Drao92]

If a system transfer function has a pole equal with 1 , j, cos(pi/4)+j*sin(pi/4) in other words its location is on the margin of the unit circle, it`s the system stable? In my opinion it`s not stable because we have a sum of 1 which doesn't converge but I am not sure. Everywhere I've read it says the poles must be inside the unit circle but it doesn't say anything about poles on the margin of the unit circle. Can somebody give me a precise answer? Thanks!
Edit: I am referring to z-plane

 

[Mark44]

If a system transfer function has a pole equal with 1 , j, cos(pi/4)+j*sin(pi/4)

What does this (above) mean?

in other words its location is on the margin of the unit circle, it`s the system stable? In my opinion it`s not stable because we have a sum of 1 which doesn't converge but I am not sure. Everywhere I've read it says the poles must be inside the unit circle but it doesn't say anything about poles on the margin of the unit circle. Can somebody give me a precise answer? Thanks!
Edit: I am referring to z-plane

What's the z-plane? Do you mean the plane z = 0?

 

[Drao92]

Iam talking about z transform and stability analysis.
Like if H(z)=z/(z-1), pole is 1. is it stable?
I have exam in 5 hours and i need an answer .