Math Is Fun Forum
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#26 2015-08-30 22:37:55
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Complex Numbers in Electronics
I just mechanically solved for z. It probably destroyed many other roots but it does find one.
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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#27 2015-08-31 00:50:24
Re: Complex Numbers in Electronics
Mechanically?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#28 2015-08-31 04:23:03
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Complex Numbers in Electronics
Yes, just get z by itself using algebra.
M is having trouble getting those roots.
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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#29 2015-08-31 12:00:31
Re: Complex Numbers in Electronics
I used M to do the sum. The answer is 10.
You are not doing the algebra right
(Z-2)^2015 = 2^2017
Or, (Z-2) = (2^(2017/2015)) w
Or, Z = 2^(2017/2015) w + 2
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#30 2015-08-31 13:25:07
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Complex Numbers in Electronics
Where does that w come from?
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.
Offline
#31 2015-08-31 20:52:32
Re: Complex Numbers in Electronics
Try guessing
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#32 2015-08-31 21:06:37
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Complex Numbers in Electronics
I am not following you.
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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#33 2015-09-01 00:18:40
Re: Complex Numbers in Electronics
That w is a complex root of unity. Do you know what that is?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#34 2015-09-01 01:11:19
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Complex Numbers in Electronics
Yes, but what is it doing in this equation.
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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#35 2015-09-01 03:00:08
Re: Complex Numbers in Electronics
When you take the nth root of something, you introduce n solutions.
For example, z^4 = 625 has roots z = 5w where w is the fourth root of unity. That is to say z = 5,-5,5i, -5i
Z-2)^2015 = 2^2017
Or, (Z-2) = (2^(2017/2015)) w
Or, Z = 2^(2017/2015) w + 2
The second line takes the 2015th root on both sides, wouldn't that introduce 2015 solutions?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#36 2015-09-01 05:38:44
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Complex Numbers in Electronics
I am sure it does have that many solutions. I did not say I had them all, I said that I got one of them.
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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#37 2015-09-01 12:51:42
Re: Complex Numbers in Electronics
Okay. Do you see the rest of the solutions now?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#38 2015-09-01 13:23:19
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Complex Numbers in Electronics
You were able to get them because I am stumped.
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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#39 2015-09-01 13:49:14
Re: Complex Numbers in Electronics
Meaning?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#40 2015-09-01 13:49:45
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Complex Numbers in Electronics
Did you get all the roots?
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.
Offline
#41 2015-09-01 13:58:46
Re: Complex Numbers in Electronics
Yes, see post 35.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#42 2015-09-01 15:13:40
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Complex Numbers in Electronics
I am not getting it.
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.
Offline
#43 2015-09-01 15:54:29
Re: Complex Numbers in Electronics
You can replace w with e^(i (2 n pi/ 2015)) where n is an integer from 1 to 2015 and i is the imaginary unit
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#44 2015-09-01 18:07:28
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Complex Numbers in Electronics
I will try that as soon as I can.
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.
Offline
#45 2015-09-01 19:57:22
Re: Complex Numbers in Electronics
There is a Vieta's solution
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#46 2015-09-01 20:03:10
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Complex Numbers in Electronics
None of those are roots.
Table[(z - 2)^2015 == 2^2017 /. z -> Exp[I ((2 n \[Pi])/2015)], {n, 1,2015}]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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#47 2015-09-02 00:37:05
Re: Complex Numbers in Electronics
There is a mistake with that code
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#48 2015-09-02 00:39:14
Re: Complex Numbers in Electronics
try this
Table[(z - 2)^2015 == 2^2017 /. z -> (2^(2017/2015) Exp[I ((2 n \[Pi])/2015)] + 2), {n, 1,2015}]'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#49 2015-09-02 00:55:37
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Complex Numbers in Electronics
That worked!
How does that affect your post #1?
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.
Offline
#50 2015-09-02 01:09:48
Re: Complex Numbers in Electronics
You can numerically do the problem now.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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