Math Is Fun Forum

aleclarsen12

Member

Registered: 2008-06-01

Posts: 36

Every math lover's dream...

I was sitting and thinking (I seen to do that alot. lol) and I had this intresting revalation:

Being in the 7th grade we concide the square root of a negative "undefiend".
Well, I dawned on me that you could just do this: sqrt(-16)=-16^1/2*sqrt(-1)

My math teacher informed me this already existed and they were called imaginary numbers. (I was crushed)

A few days later I was thinking (see what I mean) and I had another revalation. The square root of a imaganary number could be expressed as the 4th root of -1. So I wrote this formula:

A stands for alternate number line. Where N is the number line. Ex N=0 (Real Numbers) N=1 (Imaginary) N=2 (Imaginary root?) ect.

Has this already been invented? (Just crush me now)

IF NOT I HAVE FUFILED MY DREAM!!!! TO ONE WRITE MY OWN USEFUL FORMULA!! (No matter how obvious it is)

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Twitter: http://twitter.com/AlecBeta
Blog: http://AlecBeta.us.to

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Every math lover's dream...

Sorry

Roots of unity

Reinventing the wheel isn't a bad thing at all.  Just kind in mind that hundreds of people have dedicated their lives to mathematics, there is a whole lot we know, but even more we don't.

The square root of -1 is a fourth root of unity, the fourth root of -1 is an eight root of unity.  However, the complex numbers are algebraically closed.  This means that (among other things), when ever you take a root of an imaginary number, you stay within the complex numbers.  For example, an eight root of unity:

What this means is that:

But that doesn't hold for any power less than 8 and above 0.  But also:

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"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..."

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Every math lover's dream...

Hi Alec, it seems like you have a very good mind! Great thinking for someone in 7th. Keep it up.

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

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Every math lover's dream...

That's 2^n root is a nice idea because although I once knew that square rooting 4 times in a row, is the same as the 16th root, I started to forget that fact.  The only use I know of is taking the 12th root of 2 to find the ratio of frequencies in the chromatic scale, the adjacent notes.  Thanks for that reminder!!

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igloo myrtilles fourmis

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: Every math lover's dream...

I was sitting and thinking (I seen to do that alot. lol) and I had this intresting revalation:

Being in the 7th grade we concide the square root of a negative "undefiend".
Well, I dawned on me that you could just do this: sqrt(-16)=-16^1/2*sqrt(-1)

My math teacher informed me this already existed and they were called imaginary numbers. (I was crushed)

I know how you feel. Back then when I was a 7th grader myself, I realized that if you multiply two numbers whose difference is 2, the result will be the square of the middle number subtracted by 1. When I entered a math major in college I tried to write it down, only to find out that it was (a + 1)(a - 1) = a^2 - 1, an equation already well-known even before I was a 7th grader.

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.