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The square root of minus 1

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How are you with the concept of the square root of minus 1 and imaginary numbers?
I understand it 60%  60%  [ 27 ]
Bit confusing but I sort of get it 29%  29%  [ 13 ]
This makes no sense 11%  11%  [ 5 ]
Imaginary numbers; are you serious??? 0%  0%  [ 0 ]
Total votes : 45

Krabo
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03 Jun 2015, 1:26 pm

awsamb wrote:
what about i^3? do you just have -i?


Yes.



Krabo
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03 Jun 2015, 1:31 pm

Ambivalence wrote:
I understand it, but I do not believe it is founded in reality. It's a useful trick, that's all.


A trick it is, sure, but contrary to your belief, it is founded in reality. Complex numbers of the form c = a + bi can always be expressed as an ordered pair of real numbers (a, b). That's all there is. Instead of just one number, you employ a pair.



naturalplastic
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03 Jun 2015, 5:24 pm

Krabo wrote:
awsamb wrote:
what about i^3? do you just have -i?


Yes.




What about next imaginary integer? ii^3 (or however you write "the square root of negative two....cubed)?

Would that still be 'negative two'?



Krabo
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03 Jun 2015, 8:34 pm

naturalplastic wrote:

What about next imaginary integer? ii^3 (or however you write "the square root of negative two....cubed)?

Would that still be 'negative two'?


Nope. You apply standard rules of algebra, hence [√(-2)]^3 = [i(√2)]^3 = -i(√2)^3 = -2i√2.



jimmyboy76453
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04 Jun 2015, 5:41 am

I understand imaginary numbers and why they're necessary, but I've never needed to do math complex enough to use them outside school. But if it was required for my work, I could probably do it with just a little retraining.


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boredome
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05 Jun 2015, 4:49 pm

Quote:
Imagine the regular real numbers lined up single file. The positive numbers going to the right from zero (1,2,3,..), and the negative numbers going to left from zero. The "imaginary" numbers are like a second ghost family of numbers going on an axis straight up perpendicular to the line of real numbers (also starting at the zero point) going "square root of negative one", "square root of negative two", and so on.


So it's like.... two-dimensional numbers.

Whoa. That's cool


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Woodpecker
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05 Jun 2015, 5:03 pm

If you known about the Smith chart which is used in AC / RF design, then the square root of -1 makes perfect sense.

In RF electronics all impeadances have a resistive (real) and reactive (imaginary) part

Z = sqrt (R^2 + X^2)

The square root of -1 is needed to deal with things using a spreadsheet which otherwise have to be done using graph paper and smith charts.


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06 Jun 2015, 10:36 am

All kinds of numbers and other mathematical entities are abstractions. Math works by establishing abstract concepts and rules and following them consistently to find out what they lead to. The usefulness of a particular branch of mathematics comes from real-world problems it can be apply to, and it’s precisely abstraction and generality what enables math to discover patterns showing up in very different kinds of problems. Entire branches of mathematics remained a purely theoretical game for centuries, and suddenly practical applications for them were found, especially since the advent of computers.

Natural, integer, rational, real and so on are just names used to tell different abstract concepts apart. Nothing makes any of them any more real than another. The only thing you need to work with them is to be consistent. There are scientific theories making use of imaginary numbers, like classical electromagnetism and quantum mechanics, and their predictions agree with empirical evidence. If they were wrong for using imaginary numbers, the computers we all are using to post here wouldn’t work, having been designed according to those theories.

I think most of the difficulty people find in mathematical concepts comes from trying to read into them more than there actually is to them.


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17 Nov 2015, 4:31 pm

I'm doing Electronic Engineering at university and in the first year we came across these imaginary numbers. After a while I got the hang of it all, just started off simple and worked from there.

Oh, and since I was in electronics, we called it j, because I is used for currents.