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## Main Question or Discussion Point

Hi all.

I have some questions on complex analysis. They are very fundemental.

1) Singularities of a complex functions are the points, where the functions fails to be analytic. Will a singularity then always be a point, where the numerator of the functions is zero?

2) This question is on integration in the complex plane. If have a function f(z), then I have to specify the curve C (parametrized by z(t)), on which I wish to integrate f(z) along. If I just want to find the length of the curve, then which of the following integrals are correct?

[tex]

\int dz \quad \quad \text{or}\quad \quad \int z(t) dz.

[/tex]

I hope you can help. I would very much appreciate it.

Best regards,

Niles.

I have some questions on complex analysis. They are very fundemental.

1) Singularities of a complex functions are the points, where the functions fails to be analytic. Will a singularity then always be a point, where the numerator of the functions is zero?

2) This question is on integration in the complex plane. If have a function f(z), then I have to specify the curve C (parametrized by z(t)), on which I wish to integrate f(z) along. If I just want to find the length of the curve, then which of the following integrals are correct?

[tex]

\int dz \quad \quad \text{or}\quad \quad \int z(t) dz.

[/tex]

I hope you can help. I would very much appreciate it.

Best regards,

Niles.

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