- #1
Simfish
Gold Member
- 811
- 2
consider the function
\frac{1}{\epsilon^2 + z^2}
So we know that there are two poles, one at z = i \epsilon, one at z = - i \epsilon. So when this function never hits 0 on the real line, how do the singularities affect its behavior on the line?
Okay, so poles are a subclass of singularities. I think that z = i \epsilon and z = - i \epsilon are poles - I may be wrong here. The question is - how do complex singularities (complex poles in this case) affect a function's behavior when the function is plotted on the real line?
\frac{1}{\epsilon^2 + z^2}
So we know that there are two poles, one at z = i \epsilon, one at z = - i \epsilon. So when this function never hits 0 on the real line, how do the singularities affect its behavior on the line?
Okay, so poles are a subclass of singularities. I think that z = i \epsilon and z = - i \epsilon are poles - I may be wrong here. The question is - how do complex singularities (complex poles in this case) affect a function's behavior when the function is plotted on the real line?
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