- #1

monnapomona

- 39

- 0

## Homework Statement

Evaluate the integral using any method:

∫

∫

_{C}(z^{10}) / (z - (1/2))(z^{10}+ 2), where C : |z| = 1## Homework Equations

∫

_{C}f(z) dz = 2πi*(Σ

^{k}

_{i=1}Res

_{p_i}f(z)

## The Attempt at a Solution

Rewrote the function as (1/(z-(1/2)))*(1/(1+(2/z^10))). Not sure if Laurent series expansion is the best choice for this problem but I ended up getting: (Σ

^{∞}

_{n=0}(1/2)

^{n}/ z

^{n+1})*(Σ

^{∞}

_{n=0}(-1)

^{n}2

^{n}/(z

^{10})

^{n})

I get stuck at this point but i tried working out the series and get: 1 - 2/z

^{12}+ 1/z

^{23}+ ...

So would the residue just be 1 and the ∫

_{C}f(z) dz = 2πi?

**sorry in advance for my formatting**