Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20060802 03:14:14
imaginary numbersyou know, often the algebraic behavior of numbers can be used to perform some nifty tricks for things like summation. For an alternating series we can use (1)^n to change from even to odd numbers. A logarithm is just a misspelled algorithm. #2 20060802 05:16:29
Re: imaginary numbers
I believe that's supposed to read negative and positive. So we can always reduce i into a power of 1. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20060802 06:34:38
Re: imaginary numberswhoops! Yeah meant to right positive and negative. A logarithm is just a misspelled algorithm. #4 20060802 07:13:11
Re: imaginary numbers
No, because all complex numbers must take on the form: a + bi. It's how they are defined. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #5 20060802 12:17:52
Re: imaginary numberswell couldn't 5 + i^4 be written as 6 + 0i? A logarithm is just a misspelled algorithm. #6 20060802 12:39:54
Re: imaginary numbersYes, but 5 + i^4 is not in "complex form", so to say. 6 + 0i is. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #7 20060802 12:56:04
Re: imaginary numbersI think I see your point from the last statement. But uh... so what? All I said was a function that would return the real part of a complex number (Whether the imaginary coefficient is zero or not) so it can have a place value on the numberline. A logarithm is just a misspelled algorithm. #8 20060802 17:22:04
Re: imaginary numbers
well yes, i would think so. The Beginning Of All Things To End. The End Of All Things To Come. #9 20060803 00:46:40
Re: imaginary numbers
That is correct, but historically backwards.
Yep. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #10 20060803 00:56:24
Re: imaginary numbers
Yes. And that's a cool thing to do, for the reals are what is called not algebraically closed. #11 20060803 01:07:02
Re: imaginary numbersNaturals, integers, rationals, and reals are all not algebraically closed. But the complex numbers are. That makes them special. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #12 20060803 02:01:44
Re: imaginary numbers
Ah, but there's a neat trick here.
Yes, but Mikau's original point was about imaginary numbers, not complex numbers
I don't think I quite agree, but you may be right. But note the two following bits of trivia (just for fun): ......... see the pattern? Note also that the 4th power of all of these guys is +1!!. Is this true of all integer powers of i? Of course! Last edited by ben (20060803 02:10:21) #13 20060803 02:20:23
Re: imaginary numbers
My mistake. I always use those term interchangably when they really aren't. But it still holds that we would not call i^2 imaginary, right?
Well, assuming that we are talking about integer powers. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #14 20060803 02:31:09
Re: imaginary numbers
That is a subtle point, right enough. I suspect it would be a matter of taste. Hmm. Actually maybe it's a bit silly to even talk in these terms. The imaginaries are not a field, a ring or even a group, as we agreed. #15 20060803 05:08:56
Re: imaginary numbers
Not only 2i. IPBLE: Increasing Performance By Lowering Expectations. #16 20060803 05:25:08
Re: imaginary numbersWouldn't it be ±√(2) i "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #17 20060803 05:40:40
Re: imaginary numbers
Oh dear #18 20060803 06:05:41
Re: imaginary numbersI recall one calculus test I took in highschool: "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 