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Math Help - Complex analysis

  1. #1
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    Lightbulb Complex analysis

    I got a doubt on the order of zeroes of a complex function at a given point.

    My opinion is that, "At a particular pt. z1, a given complex f(z) function always has a unique number of zeroes of a given order n."

    In other words, if f(z) has zeroes of order m and n at a particular point z1, then m = n always.

    Am I correct in making this statement?
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  2. #2
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    Re: Complex analysis

    Quote Originally Posted by MAX09 View Post
    I got a doubt on the order of zeroes of a complex function at a given point.

    My opinion is that, "At a particular pt. z1, a given complex f(z) function always has a unique number of zeroes of a given order n."

    In other words, if f(z) has zeroes of order m and n at a particular point z1, then m = n always.

    Am I correct in making this statement?
    What does it mean for f(z) to have "zeroes" at a given point. f(z) is either zero at that point or it's not.
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  3. #3
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    Re: Complex analysis

    I stand corrected, romsek.

    I must have typed "In a particular domain, D".

    Barring that , is my statement valid?
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