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Complex analysis 1/(z-w)^4

  1. Mar 19, 2007 #1
    Oh god, so confused and panicked today:cry:
    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??
  2. jcsd
  3. Mar 19, 2007 #2
    (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?
  4. Mar 20, 2007 #3
    as yes, right you are, and a pole is one of the three types of singularity... removable, pole and essential!
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