Complex Integral of Absolute Value

Question

I have a hard time understanding how one can take the following complex integral. $$\int |z|^2 \, dz.$$ Why is it not path independent.

score 3 · Answer 1 · answered Nov 10 '16 at 06:10

3

Absolute value is not an analytic function, so the integral will not be path independent.

answered Nov 10 '16 at 06:10

Robert Israel

But wouldn't the hypotheses of the Fundamental Theorem of Calculus and Cauchy's Theorem apply since the function is continuous, has an anti-derivative, and is differentiable on a domain containing the path? – Ptheguy Nov 10 '16 at 06:11
2

It does not have an anti-derivative, and is not differentiable (in the complex sense). – Robert Israel Nov 10 '16 at 06:34

1 Answers1