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Complex Numbers- The Other Side of Algebra
Author: Jennifer Barlow
 Added: 03/22/2003
 Type: Tutorial
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The concept of i

Imaginary numbers can be thought of as the "other" side to algebra. We are all used to a^2 + b^2 = C^2 and D=rt. We all know that you can't get the square root of a negative... over the set of all reals! In order to understand complex numbers, one must understand the concept of i.

i^0 = 1

i =   the square root of -1

i^2 = -1

i^3 = - (square root of -1)

i^4= 1

To find the rest of  i^x, divide the exponent by 4 and use the remainder to determine what its value is.

Ex. i^44     44/4 = 11 w/ remainder of 0, so use i^0. i^44 = 1.

Ex. i^14  14/4 = 3 w/ remainder of 2. Use i^2, so i^14 = -1

 

Article Pages:  1 | 2 | Next »  
                          


  Article Comments   Add Comment | View All (4)

Poster: Chris
Added: -0/7-/2004

Isn't it safe to assume that 'i' is simply another spacial dimension? (I have always believed that common inductors and capacitors exhibit characteristics that transcend 3-D space, and thus require the introduction of an additional mathematical dimension in order to successfully work the equasions.) If you can accept the Philedelphia Experiment as fact, didn't it utilize this principle?

BTW, what's (-i)^(1/2)?
Poster: Edmont
Added: -0/6-/2003

what of i^i ; i^A*p(x)
where A e Re , p(x) function
of x ; an interesting random
walk ?
Poster: Philip
Added: -0/3-/2003

Great article Jennifer. I was going to write an article on complex numbers but you beat me to it ;)
Poster: Jennifer Barlow
Added: -0/3-/2003

Sorry everyone; in example three, the problem should read: x^3-2x+4x-8. I had accidentally typed in +8 on the problem.
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