# Complex integral

## Homework Statement

$$\oint_{L} \frac{ \mbox{d} z}{ z(z+3) }$$ and $$L:|z|=4$$

## The Attempt at a Solution

what is assumption, is it oriented positive or negative? and Cauchy formula, can it be done like this?
$$\frac{ 1 }{ 3 } \left( \oint_{L} \frac{ \mbox{d} z}{ z } - \oint_{L} \frac{ \mbox{d} z}{ z+3 } \right)$$

HallsofIvy
Homework Helper
If nothing else is said, the integral is assumed to be in the positive orientation, counter-clockwise.
Yes, your partial fraction reduction is correct and the integral can be done in that way. Letting $z= e^{i\theta}$ in the first integral and $z= 3+ e^{i\theta}$ in the second will give very simple integrals, giving the residues at z= 0 and z= 3.

thanks for answer, I got 0, is it possible? and please tell me why residue in 3, not -3?

Last edited:
up.,

Dick