# Complex Integration example

Suppose I'm asked to compute the value of the complex integral: $$\int_{C}^{}\frac{\operatorname{Log}(z)}{z}\,dz$$ with $C=[i,1].$

Is it possible to treat the complex integrand like a real one and apply the rules of integration with limits $i$ to $1$, or do I ought to parameterize the given curve and then treat it like a line integral?

• It's not clear what $C=[i,1]$ means. How are you getting from $i$ to $1$? – Adrian Keister Apr 25 '18 at 19:49
• How do you define $\log z$? – José Carlos Santos Apr 25 '18 at 19:49
• C is the line segment from i to 1 and Logz is the complex logarithm. – Jevaut Apr 25 '18 at 19:54
• @Andrew Tzevas: In that case, since your path never crosses a pole and is analytic on a domain containing the path, I think you could simply compute the antiderivative and use the fundamental theorem for line integrals. – Adrian Keister Apr 25 '18 at 20:00
• $z = \mathrm{i} + \left(1 -\mathrm{i}\right)t$. – Felix Marin Apr 25 '18 at 22:25
