Question

Is (1)/(z-i) meromorphic at C?

Answer 1

Do you see any poles?

Answer 2

yes
z= i (simple pole)

Answer 3

So it is holomorphic at the entire complex plane, with the exception of z = i.
Now what is the definition of a meromorphic function?

Answer 4

"A meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except at the poles of the function."
So the function has to be meromorphic. Thank you