Mathematics · Complex Analysis

Let f(z) be a complex-valued analytic function defined on a domain S ⊆ ℂ. Consider the following statements: A. The order of a zero of a polynomial equals the order of its first non-vanishing derivative at that zero. B. The zeros of a non-zero analytic function are isolated. C. Zeros of f(z) are obtained by equating the numerator to zero if there is no common factor in the numerator and the denominator of f(z). D. The limit point of the zeros of an analytic function is an isolated essential singularity. Which of the statements given above are correct?