- #1

handiman

- 4

- 0

## Homework Statement

Let γ denote the portion of the circle lzl = √(ln(3)) which lies in the left-half plane.

Prove l(∫

_{γ}(e^(iz

^{2})/(z-1) dz l ≤ (3pi√(ln(3))/(ln(3)+1)

Note: the l l around the integral represents modulus.

## Homework Equations

In the past we used this inequality.

l∫

_{λ}f(z)/g(z) dz l ≤ max lf(z)/g(z) l * length(lzl)

## The Attempt at a Solution

So far I found the length of lzl to be 2pi√(ln(3)) and g(z) ≥ √(3) - 1.

I am not sure about my work on g(z) and for f(z) = le^(iz

^{2}) I am very confused as to how to proceed.