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[Vector]

KingBacon, my specialty in college was topology.  You're correct, but the comment about "clopenness" detracts rather a lot from this elementary result.

[Descan]

This isn't to do with my schoolwork. That's on hold until I can shift to the next unit (bloody sick teachers and un-prepared substitutes :I)

But I've always wondered: What the hell is the point of i? What's it used for?

(I'm not saying math has to have a purpose. I love fucking with numbers. But I'm pretty sure I've seen it used in actual applications and I have no idea what those applications are or... yeah.)

[Darvi]

Two uses I can think of immediately are for electronics and geometry.

[HFS]

I believe i is used for vectors in electrical work, or something like that. Kind of important.

[ZetaX]

The usage of complex numbers in pure mathematics is something not that easily seen or described to someone not already having some knowledge in the field. So I could throw some stuff at you, but you won't be able to really understand them until much later or never (depending on your fields of study). For now you should just take these facts without evidence:

- You already seem to accept reals, but neither do the latter have any real world implementation.
- They behave very well, es they contain a lot of things and have some extra properties.
- They occur in a lot of areas like number theory, algebra, topology and analysis.

[MonkeyHead]

You will also run into i as a solution for various mechanics and physics problems which need to be solved as a quadratic (or potentially higher degree polynomial). Of course, the concept of an imaginary time or position value is a strange one indeed.

[Helgoland]

Breaking down polynoms into linear factors, and rotations (e to the power of i times phi, very useful in physics).
Off the top of my head - there are tons more.

[Zrk2]

Let me see....

Finding the limit as X approaches infinity of

The Square root of (9x^6 - X)

Divided by X^3 + 1

How do you do it? I understand the answer (afterall 9x^6's square root is essentically 3x^3... making the question 3/1)

But how do you get rid of the -x? Or does that just not matter for this question?

I am aware you COULD use a conjugate, but that seems needless

Rationalize! You'll eliminate the square root, then everything should start collecting and be easier from there.

[ZetaX]

What do you mean by "rationalize"¿ Unless that's some strange term for squaring it gives no advantage, and even the latter does not help that much. Just do as told and divide numerator and denominator by x³.

[Zrk2]

I might actually have jumped to a hasty conclusion. Actually, one could square both then use limit rules to conclude that y approaches 9 as x approaches infinity. I think.

[Virex]

Two uses I can think of immediately are for electronics and geometry.

Other examples are quantum mechanics, control theory, acoustics and optics.

[Another]

Two uses I can think of immediately are for electronics and geometry.

Other examples are quantum mechanics, control theory, acoustics and optics.

In other words - everything where something can oscillate can be very conveniently expressed using complex numbers.

[Neonivek]

Ok here is a problem I am never able to solve

Lets say you have two beakers of acid and one is 15% acid and the other is 24% acid

And you need 100 beakers worth of material that is 17% acid (or something like that)

How do you solve this?

[MagmaMcFry]

Well first of all it is impossible to get 100 beakers worth of acid using only 2 beakers worth of ingredients. But assuming you have infinite amounts of either liquid:

Let's say that you mix together x beakers of the first liquid and y beakers of the second. Then you get x+y beakers worth of liquid, containing (.15*x + .24*y) beakers of acid. To solve the problem, you need 100 beakers containing 17% acid, so you get these equations:

x+y = 100

.15*x+.24*y = .17*100

Then solve the system of linear equations and you get x = 700/9, y = 200/9.

[Pnx]

Ok, so everything I've looked at has told me that the derivative of ln(5x)= 1/x
Which is the same derivative as ln(x)... which indicates that ln(x) has the same slopes as ln(5x)...
Which is something I don't really get.
Can anyone explain to me how that one works?