[Gigglyboots]

I was more of a Modern Studies girl, probably because it was so easy..

[Console]

What's 'Modern Studies'? I don't remember doing that.

[Sidders]

Of course it's not, the square root of -1 is i (or j), just like the square root of 4 is 2 (or -2). The reason people don't understand i is because they're not used to it, it isn't a part of regular maths. Centuries ago many people felt the same way about negative numbers, how can you have minus something? However, these numbers make complete sense now-a-days. I can understand the concept of i, but it is difficult to explain as there's not a lot to compare it to. It's a bit like another realm of mathematics, only more complex.

Negative number are an easy to understand concept though. If something is negative, it is a lack of something. I have negative funds in my bank account because I owe the bank money. How can i exist in the real world when it can't be plotted on any normal graph?

[Console]

Negative isn't the lack of something, zero is the lack of something, negative means taking away something you never had to begin with. Also, i is pretty simple to plot on a graph, all you do is change one of the axis from real numbers to complex numbers.

[Sidders]

OK, to go in another direction, can you give me an example of where i occurs in the real world? I have already given an example of where negative numbers occur with my bank account example.

(We're making this thread really geeky BTW)

[donnie]

zero is not the lack of something its all relative. eg zero degrees centigrade does not mean the lack of temperture.

[Sidders]

No, it just means 0 is where they started the scale because it's the temperature which water freezes. Absolute zero (0K) is the complete lack of temperature.

[Console]

I know that i is involved in quantum physics, electromagnetism and advanced geometry, but due to the high level of maths involved it's hard to find a solid example of where they're used. Like e, gamma (golden ratio) or even c (speed of electromagnetic radiation), i is just a constant, albeit it a hard to understand one, which isn't really needed in everyday life, but does have mathematical uses.

The only example I can think of that involves i is the following:-

e^( i * (pi) ) = -1 # e to the power of i * pi equals minus one

That's not so much a useful formula as it is interesting to see three irrational numbers come together to form a rational one.

[donnie]

No, it just means 0 is where they started the scale because it's the temperature which water freezes. Absolute zero (0K) is the complete lack of temperature.

that doesn't sound right? so if it was possible to be in an environment of zero k it woudnt feel cold?

[Sidders]

It wouldn't be possible. It would feel cold yeah, but it couldn't get any colder.

[donnie]

so there would be temperature!

[Console]

0K is the point at which something has absolutely no energy, which means it emits no radiation, thermal or otherwise. It would not have a 'temperature'. It's difficult to say what it would 'feel' like because it's an impossible situation to be in, as for it to happen you too would need to be at 0K and would therefore be dead and a frozen block.

[donnie]

like jo whiley?

[Gigglyboots]

Modern Studies is like politics, it's probably a weird equivalent of General Studies, i.e. very easy.

[Console]

I never liked General Studies, which is probably why I conned my teachers into getting me out of it.

[Gigglyboots]

I loved the fact you could do that at school, but at Uni, I feel like I'm stuck with Law.. I could change, but think it's a bit too much effort now.

[Sidders]

e^( i * (pi) ) = -1 # e to the power of i * pi equals minus one

That's not so much a useful formula as it is interesting to see three irrational numbers come together to form a rational one.

I've heard of that before, but I don't understand how it can be proved.

[Console]

It's a special case of Eulers forumula:-

e^(i * x) = i * sin x + cos x

When x = pi, sin x becomes 0 and cos x becomes -1.

[Sidders]

Way too deep for me.

[Adam]

Way too deep for me.

Yeah, dont want you drowning or anything.