- #1
Amad27
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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 $2\pi$