NationStates Jolt Archive

Hi, I lurk here sometimes lol, but I just wanted to post this to see what you guys think:

My math teacher started talking to us today about imaginary numbers, and she stated that every number is complex (meaning they're in the form a + bi). But then I was wondering, what happens if you raise i to the i-th power? Is that an imaginary number too, or is that some really weird thing? Does anybody know what that would look like, or anything?










Ah yes, i forgot: :sniper::sniper::sniper:

Yes, it is still "imaginary." *racks brain trying to remember the interpretation of i as an exponent*
There's a famous equation relating all the fundamental constants in math:
(hard to write this without superscripts)
e to-the-(i-times-pi) plus one equals zero.

And here's a real* math joke to try on your instructor:

What is infinity times i? Eight. (Ask her to explain it ;) )

*Aren't there some provocative names for things in math? :p

Using Euler's formula: (e^ix) = cos x +(i)(sin x)

Substitute pi/2 for X

you get that e^(i(pi)/2) = i

Raise both sides to the i power. The i exponent on e becomes squared. Thus, it is equal to negative one.

So:

i^i = e^(-(pi)/2) (About 0.27078)

where e is the base of the natural logarithm (the limit of (1+ 1/n)^n as n approaches infinity) (About 2.71828)

Where I got the proof from:

http://en.wikipedia.org/wiki/Imaginary_unit#i_and_Euler.27s_formula

I guess e^-(pi/2) could be considered a weird number.

Take a course in calculus if you ever get the chance. Its terribly fascinating stuff on a conceptual level.

THe only math (http://www.schoolhouserock.tv/Multiplication.html) you ever need.

an answer
[checks the complex numbers book]
That is correct

THe only math (http://www.schoolhouserock.tv/Multiplication.html) you ever need.

I agree. when do we use imaginary numbers? when we're counting imaginary money? I never had the slightest desire to continue past trig.

when do we use imaginary numbers?wave propagation

What is infinity times i? Eight. (Ask her to explain it ;) )
I actually got that. I don't know whether to feel proud or embarrassed...

Also, according to the Google (http://www.google.com/search?hl=en&q=i%5Ei&btnG=Google+Search), the answer is indeed 0.207879576 (or roundabout that). And yes, Google's built-in calculator handles imaginary numbers. :p

Using Euler's formula: (e^ix)= sin x + (i)(cos x)

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

[/math nazism]

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

[/math nazism]

Thanks for clearing that up; I got 1 out of the old formula, not i.

Frankly, the geekiest math problem I figured out is this:

Take every person on the planet (about 6.5 billion people.) Pluck them into a world where they stay alive forever and never reproduce. Split them into groups of four. Deal each group of four a hand of bridge. Repeat this process every four minutes until the end of time.

On average, a perfect hand will be dealt once every 10.5 trillion years.

I agree. when do we use imaginary numbers? when we're counting imaginary money? I never had the slightest desire to continue past trig.

Well, you should probably be thankful for imaginary numbers since they help hold the universe together. :p

THe only math (http://www.schoolhouserock.tv/Multiplication.html) you ever need.

Plus this:

Some of you who have small children may have perhaps been put in the embarrassing position of being unable to do your child's arithmetic homework because of the current revolution in mathematics teaching known as the New Math. So as a public service here tonight, I thought I would offer a brief lesson in the New Math. Tonight, we're gonna cover subtraction. This is the first room I've worked for a while that didn't have a blackboard, so we will have to make do with more primitive visual aids, as they say in the ed biz. Consider the following subtraction problem, which I will put up here: 342 minus 173. Now, remember how we used to do that:

Three from two is nine, carry the one, and if you're under 35 or went to a private school, you say seven from three is six, but if you're over 35 and went to a public school, you say eight from four is six ...and carry the one, so we have 169.

But in the new approach, as you know, the important thing is to understand what you're doing, rather than to get the right answer. Here's how they do it now:

You can't take three from two,
Two is less than three,
So you look at the four in the tens place.
Now that's really four tens
So you make it three tens,
Regroup, and you change a ten to ten ones,
And you add 'em to the two and get twelve,
And you take away three, that's nine.
Is that clear?

Now instead of four in the tens place
You've got three,
'Cause you added one,
That is to say, ten, to the two,
But you can't take seven from three,
So you look in the hundreds place.

From the three you then use one
To make ten ones...
(And you know why four plus minus one
Plus ten is fourteen minus one?
'Cause addition is commutative, right!)...
And so you've got thirteen tens
And you take away seven,
And that leaves five...

Well, six actually...
But the idea is the important thing!

Now go back to the hundreds place,
You're left with two,
And you take away one from two,
And that leaves...?

Everybody get one?
Not bad for the first day!

Hooray for New Math,
New-hoo-hoo Math,
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!

Now, that actually is not the answer that I had in mind, because the book that I got this problem out of wants you to do it in base eight. But don't panic! Base eight is just like base ten really - if you're missing two fingers! Shall we have a go at it? Hang on...

You can't take three from two,
Two is less than three,
So you look at the four in the eights place.
Now that's really four eights,
So you make it three eights,
Regroup, and you change an eight to eight ones
And you add 'em to the two,
And you get one-two base eight,
Which is ten base ten,
And you take away three, that's seven.
Ok?

Now instead of four in the eights place
You've got three,
'Cause you added one,
That is to say, eight, to the two,
But you can't take seven from three,
So you look at the sixty-fours...

"Sixty-four? How did sixty-four get into it?" I hear you cry! Well, sixty-four is eight squared, don't you see? "Well, ya ask a silly question, ya get a silly answer!"

From the three, you then use one
To make eight ones,
You add those ones to the three,
And you get one-three base eight,
Or, in other words,
In base ten you have eleven,
And you take away seven,
And seven from eleven is four!
Now go back to the sixty-fours,
You're left with two,
And you take away one from two,
And that leaves...?

Now, let's not always see the same hands!
One, that's right.
Whoever got one can stay after the show and clean the erasers.

Hooray for New Math,
New-hoo-hoo Math!
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!

Come back tomorrow night...we're gonna do fractions!

Y'know, I've often thought I'd like to write a mathematics textbook someday because I have a title that I know will sell a million copies; I'm gonna call it Tropic of Calculus.

0.9 recurring = 1

arnt i clever :p

is i the square root of -2?

0.9 recurring = 1

arnt i clever :p

is i the square root of -2?

i=sqrt{-1}

0.9 recurring = 1

arnt i clever :p

is i the square root of -2?

No, it's the square root of -1.

i=sqrt{-1}

No, it's the square root of -1.

cheers for clearing that up.

what is sqrt of -2 then?

cheers for clearing that up.

what is sqrt of -2 then?

(sqrt{2})i

I agree. when do we use imaginary numbers? when we're counting imaginary money? I never had the slightest desire to continue past trig.

I'll probably need calculus for programming, but I don't wanna :(

thanks again

I'll probably need calculus for programming, but I don't wanna :(

If you take more math now, it's less you have to take later. I took AP Calculus in high school and struggled for a C with one of the toughest teachers I've ever had...but thanks to her, I got a 5 on the exam and didn't have to take math in college. (But like a dummy, I did anyway, though the professor was more of a Doc Brown figure and wasn't anywhere near as tough.)

I've also concluded that Google's calculator can calculate numbers as high as (2^1024)-1. However, if you plug that number in, it craps out because it has to calculate (2^1024) first, and that's too high. And it's too damn long to calculate (2^1023) + (2^1022) + (2^1021) ... (2^2) + (2^1) + (2^0). I suppose I could calculate the sum of all terms of (2^(1024-x)) for 1 <= x <= 1024.

Mathematics is the work of the devil.

Mathematics is the work of the devil.

No, just geometry.

when do we use imaginary numbers?

"Love Is An Imaginary Number."

Mathematics is the work of the devil.

Science H. Logic damn you!

I actually got that. I don't know whether to feel proud or embarrassed...

You should feel both ;)

You should feel both ;)

Same here...count me in as adding a +1 to my Uber-Dork rating.

I agree. when do we use imaginary numbers? when we're counting imaginary money? I never had the slightest desire to continue past trig.

Inductance, capacitance. Its kinda hard to explain opposition to current that does not involve any loss of energy.

Plus if you go into higher order math and sciences, they do quite simply hold the universe together. They technically do not exist (hence the name "imaginary") but if you did not use them, there would be no way to describe certain things.

And I corrected my transcription of Euler's equation.

:eek: *runs away from teh maths!*