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In this thread, f is assumed to be a function mapping complex numbers to complex numbers, unless it is explicitly stated otherwise.

#1

**Click here for the video solution.**

*Last edited by zetafunc (2015-10-24 08:12:21)*

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#3

*Last edited by zetafunc (2017-04-03 22:37:57)*

**LearnMathsFree: Videos on various topics.New: Integration Problem | Adding FractionsPopular: Continued Fractions | Metric Spaces | Duality**

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#4

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#5

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#6

*Last edited by zetafunc (2016-08-08 08:32:28)*

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#7

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#8

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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*Last edited by zetafunc (2015-07-20 00:10:56)*

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*Last edited by zetafunc (2015-07-20 00:11:26)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

Thanks for the answers and method.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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No problem, I can post the solutions to others if you would like. #6 is basically a generalisation of the method used in post #14.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

Post them at your convenience.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Update: Have started making video solutions to the problems. A solution to #1 has been recorded.

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A video solution has been added for #2.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

I am watching the video now.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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I've also added a video solution for #6, for n = 8. The case for general n is done in exactly the same way (that is, the idea of choosing a contour that encloses just one of the poles).

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