I could explain it, but it's kinda complex... Appalling puns aside, what's with the interest in dem imaginary numbers?
It is some stupid, retarded mathematician that wanted to fuck with people. I think he ended up going crazy and killing himself. Why do you care? Are you going for electrical engineering? I can only imagine you getting a degree in communication or business.
Specifically, what are they asking for this "college level algebra" (i.e. I'm-insecure-about-taking-intro-algebra-in-college Algebra) test? Don't tell me it's, "how the fuck do you do complex numbers?" If that's what they're asking, you should probably look into a different college. Anyway, I doubt you're doing much more than just basic manipulation of i and roots of negative numbers. Just remember i^2=-1. And yeah, that's pretty much all you need to know. Make me proud.
Treat them like the literal coefficients in any other polynomial, except that they equal to sqrt(-1). Now if you suck at polynomials, then yer fuhked.
That's actually not difficult. You need basic calculus and you can get a legitimate proof: http://mathrefresher.blogspot.com/2007/10/shorter-proof-of-eulers-formula.html I'm sure you could jury rig a proof with high school algebra if you used some math contest tricks (i.e. batshit insane stuff). It wouldn't be as short as the above proof, but I bet it could be done. If you want a better challenge, prove that the sum of n cubed natural numbers (i.e. (1^3+2^3+3^3+4^4+...+n^3)) equals the sum of n natural numbers squared (i.e. (1+2+3+4+...+n)^2). I had to do that last quarter...
Ah, first cuz I remember doing college algebra in high school (oddly, while taking algebra II at the same time) and doing complex numbers for a week or two. Aside from what ImSpartacus said and remembering that all complex numbers have a real and imaginary component, you should be fine. Actually, I remember this from college algebra: i^1 = i i^2 = -1 i^3 = -i i^4 = 1 i^5 = i i^6 = -1 ... Though all of that can be derived from i^2 = -1
I spoke with Commie on this. He has simple as shit questions like y=mx+c (basic linear functions) next to complex numbers, which I've actually never been taught. It's just totally lopsided. Stuff I learnt when I was 11 vs stuff people (in the UK at least) who are doing advanced mathematics are learning at the age of 17/18, in the same exam.
Tests like that are meant to cover everything. They will touch on the lowest of the low, but also the highest, most irritating problems. Like in the ACT (an American standardized test for entrance into universities and stuff) math section. There are some very easy problem, but there's always one logarithm problem. Most kids don't learn logarithms in high school. I had to ask my math teacher to help me learn logarithms so I would be able to stand a chance of getting just one more fucking problem correct. So it probably isn't a big deal if he can't do those handful of problems. But if you shot me a link to the exam, I'd be happy to help with it. I'm on winter break now, so I have a lot more time to screw around. If d=1,o=2 and g=3, then absolutely. Here, take a sticker.
See that's interesting too. We didn't do complex numbers but we did logarithms quite early on, so the differences are quite interesting.
algebra? I might be a little off on this because naming in polish is a little diffrent, but isnt that like x's and y's and shit? I had calculus last year, and now that is some hard shit.
They don't teach complex numbers until you're 17/18? For us, that'd be 12th grade. I learned complex numbers back in 9th grade when I was 14/15 years old. I learned logarithms next year, but that's because I taught myself, them. Most students didn't learn them until 11th grade. I do have to ask though, do you guys learn matrices and/or parametric equations in high school? We skipped matrices entirely and are only lightly touching on parametric equations.
At that level, you're just being barely introduced to any of those things. I mean, I could teach Intro to Set Theory to an 8th grader, and they would be able to say that they understand sets, but that doesn't mean that they understand any of the applications of basic Set Theory. What I'm saying is that just because you're kickass as using a hammer doesn't mean you can build a house. Knowing how to use the tools is essential, but applying them can be pretty intense.
Matrices are taught around the same time/area as Complex numbers. And again, like complex numbers, they're only taught to the guys who do "Further Maths" rather than regular maths. It's an entirely separate qualification. Parametrics though we got taught much earlier, probably around 14-16 area, and pretty in-depth iirc.
What, exactly, do you mean by applications of things like logarithms and complex numbers? From a practical point of view, as they apply in the real world, or from a mathematical point of view, as in knowing how and when to use them in equations and how to manipulate them?
