Understanding Poles and Zeros in Complex Analysis

[Ant farm]

Oh god, so confused and panicked today
I know this is a very basic question, but, givin the function 1/(z-w)^4

does this have one pole of order 4, or possibly 4 poles of order 1...?

Also, could you please clarify,
''to get the zero's of a function, set the numerator = 0''
''to get the poles of a function, set the denominator = 0''
is this correct??

 

[moo5003]

(z-w)^4 is 0 iff z=w. So, it has one pole at w.

I always though when the denominator was 0 it was referred to as a singularity?

 

[Ant farm]

as yes, right you are, and a pole is one of the three types of singularity... removable, pole and essential!