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MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Euler's Formula for Complex Numbers

Had a go at explaining Euler's Formula for Complex Numbers

What do you all think?

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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: 10,140

Re: Euler's Formula for Complex Numbers

hi MathsIsFun,

Another great page!  Well done!

I wish I could turn the clock back and get the inventor of 'imaginary numbers' to call them something else.  It has led to the unfortunate idea, held by some, that imaginary numbers have less validity than 'reals', because they are made up and don't really exist (whatever that means).

I believe that the proper reason for this name is that the second axis on the Argand diagram is the image of the first. Possibly you could add a note to this effect?

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Euler's Formula for Complex Numbers

Hi MIF;

Thanks for the page.

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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: 7,711

Re: Euler's Formula for Complex Numbers

I believe that the proper reason for this name is that the second axis on the Argand diagram is the image of the first.

That would be a nice reason, but I believe "imaginary" was used to ridicule them, until they found the complex realm was a hidden truth behind many things.

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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: Euler's Formula for Complex Numbers

Hi;

Some books give the credit to Descartes who was ridiculing them.

In 50 A.D., Heron of Alexandria studied the volume of an impossible section of a pyramid.  What made it impossible was when he had to take √(81-114).  However, he deemed this impossible, and soon gave up.

Issac Newton agreed with Descartes, and Albert Girad even went as far as to call these, “solutions impossible”

Interesting!

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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.