Layman's Explanation on Imaginary Numbers?

MacIver · #1 by **MacIver** » Aug 05, 2011 3:30 am

Imaginary Numbers have always confused me.

I get that their squares are negative. And I understand a good way to picture them is on the Y axis if the X axis is Real Numbers. But beyond that I'm completely baffled. What are their practical uses? Do they play any important roles in equations with real numbers? And.... what are they? :eh:

My maths knowledge is limited to my secondary (high) school education... so I'd appreciate if explanations were kept simple.

:cheers:

CdesignProponentsist · #2 by **CdesignProponentsist** » Aug 05, 2011 3:38 am

MacIver wrote:Do they play any important roles in equations with real numbers? And.... what are they?

MacIver · #3 by **MacIver** » Aug 05, 2011 3:41 am

Fractals?

Now I'm really confused!

MacIver · #4 by **MacIver** » Aug 05, 2011 3:43 am

Nice pic by the way. Stolen for my desktop.

CdesignProponentsist · #5 by **CdesignProponentsist** » Aug 05, 2011 3:56 am

Yes, it is a fractal. In particular, it is the Mandelbrot Set. It is plotted using both real and imaginary numbers. Real represented in the x axis and imaginary in the y axis. This mathematical object has shown us so much about the new type of geometry as well as the practically limitless power of recursion.

zn+1 = zn2 + c results in infinite complexity

logical bob · #6 by **logical bob** » Aug 05, 2011 1:39 pm

Don't get hung up on asking what complex numbers are. Do you feel confident about what negative numbers are? The point isn't so much that complex and negative numbers correspond to something out there in the real world as that they give us a language that can be used to talk about the real world.

I'm not really clued up on the specific real world applications. Pure maths was always my thing. In any situations where you're dealing with polynomial equations, equations like

x3 + 2x2 - 3x + 1 = 0

you're dealing with complex numbers. If you only allow x to be a real number then some polynomials don't have any solutions. At the simplest level

x2 + 1 = 0

will fail. All such failures come down to the problem of negatives having square roots, so if x can be complex there is always at least one solution. The up yourself way of putting this is that the complex numbers are the algebraic closure of the real numbers.

Pure mathematicians don't like special cases and being unable to do stuff so they're naturally drawn to working in the complex numbers for the sake of generality. Also, calculus using complex numbers is actually really nice, in the sense that it works out far more neatly and aesthetically satisfying than calculus with real numbers. There are general results which hold that simply don't work out in the reals.

Zwaarddijk · #7 by **Zwaarddijk** » Aug 05, 2011 1:43 pm

Imaginary numbers can be used to keep track of voltage and phase in AC electrical engineering.

rEvolutionist · #8 by **rEvolutionist** » Aug 05, 2011 1:46 pm

Imaginary numbers are just that. Imaginary. Like when you think of your friend's telephone number and the numbers appear in your head. Those are imaginary numbers. Real numbers, on the other hand, are real.

Hope that helped clear up your confusion.

95Theses · #9 by **95Theses** » Aug 05, 2011 4:06 pm

rEvolutionist wrote:Imaginary numbers are just that. Imaginary. Like when you think of your friend's telephone number and the numbers appear in your head. Those are imaginary numbers. Real numbers, on the other hand, are real.

Hope that helped clear up your confusion.

Where did you get this nonsense from?

Thinking of your friends telephone is a real number, thinking of your cats mobile phone number, now thats an imaginary number

rEvolutionist · **#10** by **rEvolutionist** » Aug 05, 2011 4:08 pm

I mind meld with my cat. No need for telephones. :coffee:

laklak · **#11** by **laklak** » Aug 05, 2011 4:10 pm

You cannot tell whether or not the cat has a phone number until you call it.

rEvolutionist · **#12** by **rEvolutionist** » Aug 05, 2011 4:12 pm

You guys have hijacked this thread.

cavarka9 · **#13** by **cavarka9** » Aug 05, 2011 4:32 pm

let me try(not sure), when you add positive number to a positive number, you get a positive number, when you remove a bigger positive number from a small positive number, you end up with a negative number.
But now, you can only add a positive number or remove a positive number from your negative number. You are unable in a sense to remove a negative of the negative number in your hand. If you try so, you split it and you end up with a different dimension from what you started.

Zwaarddijk · **#14** by **Zwaarddijk** » Aug 05, 2011 5:45 pm

cavarka9 wrote:let me try(not sure), when you add positive number from a positive number, you get a positive number, when you remove a bigger positive number from a small positive number, you end up with a negative number.
But now, you can only add a positive number or remove a positive number from your negative number. You are unable in a sense to remove a negative of the negative number in your hand. If you try so, you split it and you end up with a different dimension from what you started.

The idea of "a negative of a negative number" doesn't necessarily lead to imaginary numbers.

cavarka9 · **#15** by **cavarka9** » Aug 05, 2011 5:52 pm

Zwaarddijk wrote:
cavarka9 wrote:let me try(not sure), when you add positive number from a positive number, you get a positive number, when you remove a bigger positive number from a small positive number, you end up with a negative number.
But now, you can only add a positive number or remove a positive number from your negative number. You are unable in a sense to remove a negative of the negative number in your hand. If you try so, you split it and you end up with a different dimension from what you started.

The idea of "a negative of a negative number" doesn't necessarily lead to imaginary numbers.

why dont you try.

orpheus · **#16** by **orpheus** » Aug 05, 2011 5:57 pm

(Uncle Orph'sTM popcorn - "An infinity of kernels in every box" )

cavarka9 · **#17** by **cavarka9** » Aug 05, 2011 6:10 pm

one way to explain to a lay man is to tell them to stop being so lazy and go work it out them selves

BlackBart · **#18** by **BlackBart** » Aug 05, 2011 6:38 pm

rEvolutionist wrote:I mind meld with my cat. No need for telephones.

'Mind meld'. Is that what they calling it these days?

Zwaarddijk · **#19** by **Zwaarddijk** » Aug 05, 2011 11:11 pm

cavarka9 wrote:
Zwaarddijk wrote:
cavarka9 wrote:let me try(not sure), when you add positive number from a positive number, you get a positive number, when you remove a bigger positive number from a small positive number, you end up with a negative number.
But now, you can only add a positive number or remove a positive number from your negative number. You are unable in a sense to remove a negative of the negative number in your hand. If you try so, you split it and you end up with a different dimension from what you started.

The idea of "a negative of a negative number" doesn't necessarily lead to imaginary numbers.

why dont you try.

-(-x) == x

why don't I try what?

cavarka9 · **#20** by **cavarka9** » Aug 06, 2011 12:55 am

A- B means, you are removing B from A, A -(-B)=A-(-(B)) means A+B, that you are removing (-(B)), which is removing the removal of B from A. Which is basically, you are adding a positive number. So, I am just saying that either way, you are either adding a positive number or removing a positive number.