- #1

undergradphys

- 19

- 0

**1. let C be the circle |z| = 2 traveled once in the positive sense. Computer the following integrals...**

a.∫

a.∫

_{c}ze^{z}/(2z-3) dz## Homework Equations

I am confused as to a step in my solution, but i believe a relevant equation is if i am integrating over a circle and the function is analytic at a point, i can remove it by integrating and removing the denominator and replacing it with 2pi*i in the numerator. However i do not know why. This seems to be a product of the cauchy reimann equations used to calculate the integral.

## The Attempt at a Solution

So i need to get the equation in the form x/z-z

_{0}so i divide everything by 2.

I am left with .5*ze

^{z}/(z-(2/3)) In this form i can see it is analytic at z=3/2 (i believe the word analytic to mean that it goes to infinity)

so i remove the denominator, and replace it with a substitution of 2pi*i...

2pi*i*.5*z*e

^{z}evaluated at z=3/2

is equal to 3/2pi*i*e

^{3/2}

Correct? i Know that sometimes the factor 2pi*i can be negative but i dont understandw hy..