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#1 2010-05-16 01:49:30

Identity
Member
Registered: 2007-04-18
Posts: 934

Complexifying a problem

I'm trying to get the integral of

by factoring, partial fractions, and finally integration.

Here's where I'm up to so far

Now I have a feeling that this approach should work. I've been using complex numbers a lot recently and they've never failed me in all kinds of ridiculous tasks. So where do I go from here, if it is possible to go from here?

Thanks

Last edited by Identity (2010-05-16 01:49:51)

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#2 2010-05-16 02:34:15

ZHero
Real Member
Registered: 2008-06-08
Posts: 1,889

Re: Complexifying a problem

If u can express your already complex expression in the Polar Form i.e. R.e[sup]iθ[/sup], then you can probably take the Complex Natural Log and change it to form logR+iθ.

I'm not sure if it will help you Simplifying your problem any further...


If two or more thoughts intersect, there has to be a point!

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#3 2010-05-16 02:53:36

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Complexifying a problem

Thanks ZHero, I'm not sure what to do with the absolute value signs though. It acts as the modulus doesn't it? And everytime I evaluate the modulus of the stuff it comes out to be 1 hmm

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#4 2010-05-16 03:50:32

ZHero
Real Member
Registered: 2008-06-08
Posts: 1,889

Re: Complexifying a problem

Yes! It does! Coz log of -ves are "Not Defined" (you can't blame Napier for that, except for, in case, he was Napping lol)!

Try entering "alternate <space> form <space> your log expression" into WolframAlpha and look at various Alternative Representations!


If two or more thoughts intersect, there has to be a point!

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#5 2010-05-16 03:53:41

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

Re: Complexifying a problem

Hi identity;

You have taken a wrong turn somewhere that answer is not simplifed at all . Please rework the problem. No help from wolfram alpha. I do not think that is the right answer.


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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#6 2010-05-16 13:44:22

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Complexifying a problem

lol bobbym this is just some fun. I know the answer is

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#7 2010-05-16 14:09:14

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Complexifying a problem

Identity wrote:

Thanks ZHero, I'm not sure what to do with the absolute value signs though. It acts as the modulus doesn't it? And everytime I evaluate the modulus of the stuff it comes out to be 1 hmm

There are no "absolute values" in complex analysis, only modulus.

The modulus of z is 1, as you said.  This has to happen, otherwise you'll get a nonreal result.  Now just calculate the arg(z) by finding the real and imaginary parts, z = a + bi, and then arg(z) = arctan(b/a).


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#8 2010-05-16 15:54:50

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

Re: Complexifying a problem

Hi identity;

Well you got me! I was wondering why you expanded the denominator when it already was in perfect form for you. I know you know better than that.


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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