What's the meaning of a complex zero/pole?

1. What does it mean if a pole is zero?
2. What is zeros and poles in complex analysis?
3. What are complex number poles?
4. What is a zero in complex analysis?

What does it mean if a pole is zero?

Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively.

What is zeros and poles in complex analysis?

A zero of a meromorphic function f is a complex number z such that f(z) = 0. A pole of f is a zero of 1/f. If f is a function that is meromorphic in a neighbourhood of a point of the complex plane, then there exists an integer n such that.

What are complex number poles?

DEFINITION: Pole A point z0 is called a pole of order m of f(z) if 1/f has a zero of order m at z0. Identifying Poles and Zeroes. Let f be analytic. Then f has a zero of order m at z0 if and only if f(z) can be written as f(z) = g(z)(z − z0)m where g is analytic at z0 and g(z0) = 0.

What is a zero in complex analysis?

The zeros of a complex analytic function are points in the domain of function, for which the given function vanishes at that point. The singularity of a function means those points in the domain of a complex function where the function ceases to be analytic.