1. ## 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?

2. ## Re: Complex analysis

Originally Posted by MAX09
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.

3. ## Re: Complex analysis

I stand corrected, romsek.

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

Barring that , is my statement valid?