Math Is Fun Forum

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Complex Plane

First version of Complex Plane

I feel it could be improved ...

(Also, do you like the explanation of complex numbers, or prefer the one on this page: Complex Numbers)

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Complex Plane

Hi MIF;

I think the Complex Plane one will go over better. I do think it needs to be split into a couple of pages.

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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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Complex Plane

Waiting for the hypercomplex plane to come soon

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'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.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Complex Plane

I do think it needs to be split into a couple of pages.

I think so too ... maybe move all the multiplication sections?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Complex Plane

Hi MIF;

That would work.

---

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Complex Plane

hi MathsIsFun

The page is good and the explanations work well.  Ideally, a student who is new to this should read the complex number page first; but may stumble on this one first.

Suggestion: 

Keep the existing complex number page (1) as it is but add links to the complex plane page (2) and a 'Multiplying by i' page (3).

Edit the complex plane page (2) so that immediately after this (It is also called an "Argand Diagram") you have a note that advises the reader to look at  (1) first.  Then take everything from Multiplying By i onward to a new page (3)

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Complex Plane

Good advice.

The new page would be "Complex Number Multiplication" ... it will need a quick intro to complex numbers, a quick intro the complex plane ... and I cover (a+bi)(c+di) multiplication on the Complex Number page, so I should bring that in as well ... eeek.

Well I will get started on rehashing and see where it takes me.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Complex Plane

OK ... wrote a new page: Complex Number Multiplication

It would be really nice if everyone could check it for errors ... or simply make suggestions.

There seems to be disagreement on which form is the real De Moivre (with or without r): which is right for you? Have I got it correct?

I also say "for any integer exponent n": thoughts?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Complex Plane

Hi;

Abraham de Moivre, if only he had stuck to generating functions...

That is de Moivre's formula as I know it. Wikipedia has it that way too. What references do not?

For any integer n is okay. There are multiple values for non integers.

It looks good to me.

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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.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Complex Plane

Has "r": http://www.encyclopediaofmath.org/index.php/De_Moivre_formula

Has "r": http://faculty.uml.edu/klevasseur/math/demoivre/demoivre.html

No "r": http://en.wikipedia.org/wiki/De_Moivre%27s_formula

Eeek

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Complex Plane

hi MathsIsFun,

That page looks great to me. 

When I was taught de Moivre it had the r.  It's more useful like that and it's easy to 'drop' the r if desired, so I would keep it as you have written it.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Complex Plane

I prefer it with "r" too. Let's just ignore Wikipedia

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Complex Plane

hi MIF,

I've had a 'google' and the points are just about even between the two versions.  I found two 'histories of' and the score there was 1:1.  So I'm with you on this.  You can't go wrong if you follow the advice of Lewis Carroll:

“When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Complex Plane

Great page, but I suggest keeping both of them.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Complex Plane

Hi;

Maybe a picture and a little bit about Abraham de Moivre. So few students today no anything about the history of math, the stories, the people.

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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.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Complex Plane

Most people barely know much of actual pure math, much less the history of it.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Complex Plane

The 2 go hand in hand. Without knowing the history and the people it just seems like an extraordinarily hard puzzle, something abstract and foreign. Math is put into its proper prospect when you learn about the men/women who did it and why.

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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.