- #1

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## Homework Statement

##\int_{0}^{2\pi} cos^2(\frac{pi}{6}+2e^{i\theta})d\theta##. I am not sure if I am doing this write. Help me out. Thanks!

## Homework Equations

Cauchy-Goursat's Theorem

## The Attempt at a Solution

Let ##z(\theta)=2e^{i\theta}##, ##\theta \in [0,2\pi]##. Then the complex integral above becomes

\begin{align}

\int_{c}cos^2(z+\frac{\pi}{6})dz \quad \text{s.t. C:}z(\theta)=2e^{i\theta}, \quad \theta \in [0,2\pi]

\end{align}

Since ##cos^2(z)## is an entire function and ##C## is a simple closed contour, then by the Cauchy-Goursat Theorem the integral evaluates to zero.