- #1

Amad27

- 412

- 1

## Homework Statement

First, let's take a look at the complex line integral.

**What is the geometry of the complex line integral?**

If we look at the real line integral GIF:

[2]: http://en.wikipedia.org/wiki/File:Line_integral_of_scalar_field.gif

The real line integral is a path, but then you make a 3d figure, and it is the area under the 3d shape.

What about for complex integral?

And

In the problem from Schaum's Outline:

[1]: http://i.stack.imgur.com/U65As.png

This is an interesting complex analysis problem;

****The figure on the bottom left is what is being referred to,Fig7-10.****

How is in the solution:

$$\int_{BDEFG} = \int_{0}^{2\pi} \frac{(Re^{i\theta})^{p-1}iRe^{i\theta} d\theta}{1 + Re^{i\theta}}$$

How is the integral around the $$BDEFG$$, the same as the area from$$ 0 \to 2\pi$$

Thanks.

## Homework Equations

Above

## The Attempt at a Solution

$$\int_{BDEFG} = \int_{0}^{2\pi} \frac{(Re^{i\theta})^{p-1}iRe^{i\theta} d\theta}{1 + Re^{i\theta}}$$

How is the integral around the $BDEFG$, the same as the area from 0 to $2\pi$