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#1 Re: This is Cool » i = i^x mod 4 » 2014-09-23 02:23:41

Your way seems to make sense and show how it works... thank you!

#3 Re: This is Cool » i = i^x mod 4 » 2014-09-06 13:20:55

I don't understand any of that, but thank you for the input!

I was mainly interested in the idea of multiple orders of i's, each coming from its previous form (i.e. √-1, √-i, √-√-i, etc.) and their behavior (that is if the x mod 4 power rule still works for them, or if it's slightly changed), and if these special behaviors exhibit patterns.

#4 Re: This is Cool » i = i^x mod 4 » 2014-09-04 02:52:39

Sorry! I forgot to add the ^x ...

Actual theorem:

Sometimes little things get out sight..... but I think that happens to everyone.

#5 Re: Introductions » ɑβγ » 2014-09-04 02:41:18

Hello bob bundy!  And it's okay, I used to have an old account on here, but I haven't been on in so long that I just made a new one since everything was just overwhelming me: moving, homeschoolwork, learning languages (spending hours on it), learning math ( big_smile ), etc.

As far as "dx" goes, it can be interpreted as an emoticon, such as "XD", "XP", or "cx", usually showing excitement, happiness, or silliness, or it can be an infinitesimal value, i.e. the "dx" after a function in an integral, or part of a derivative written in Leibniz notation.

anonimnystefy wrote:

Is this the real life?
Is this just fantasy?

Is the Matrix reality?

I don't know if this is the real life, since the real life can be easily defined, and at times this life that we (everyone) lives in is easily defined, but at other times it's hard to understand.
As far as this being fantasy, I don't know.  It could be, it might not, who knows?
The Matrix might be reality, but it might not.  Again, who knows?

#6 Re: This is Cool » i = i^x mod 4 » 2014-09-04 02:28:40

It was just an example to show the (1/x)th root of i can be reduced to one of the 4 forms of i, and since roots and powers of i can be defined, logarithms of i can be defined, since logarithms are just fancy, difficult forms of powers and roots.

#7 Re: Introductions » ɑβγ » 2014-09-03 04:24:40

Let me rephrase my definition of reality...

Pretend "X" is a weird idea no one likes.  Okay?  Everyone thinks "X" is a myth, but in all actuality, it's real.  This means once you accept "X" as real, you accept reality, since "X" is actually real.  Once you accept reality though, (i.e. you accept idea "X") you realize "X" has nothing to do with anything, it's a useless idea, but it's an idea nonetheless.  Therefore, idea "X" is simply something that can only be understood once you accept it as real.  If you don't accept "X", you don't accept reality, therefore causing the non-existence of "X", since you don't think it's real.  In your mind you don't think "X" is real so you "block" the idea of "X" and everything about "X" out and think everything that is not "X", which is everything that is false.  Once you understand that "X" is the real deal, it's the only thing that is true, you learn that everything you know is wrong, and everything you were used to, "everyday reality", i.e. what everyone thinks, knows, etc., is actually just a big lie.  "X" is the only truth, and since it's the only real thing, idea "X" is reality.

...

Which basically means reality is just anything that is actually true, whether or not it's thought of as true.

Example:

1/0 = ∞

Most people either agree or disagree on whether this equation is true or false.  There are two outcomes, the equation is true, and everyone was right, or it's false and everyone was wrong.  The two possible answers are the "everyday realities", what everyone thinks is right.  The actual answer of whether it's true or false is true reality, and it does and doesn't exist at the same time, because if it existed, then this equation would have a definite, easy to understand answer: it's true, or it's false.  But since it doesn't, the true reality doesn't exist in this "region", and everyone is just gonna have to live with the boring answer of "IDK."

That is my best definition of reality; what is true but might not be accepted or understood.

#8 Re: This is Cool » i = i^x mod 4 » 2014-09-03 04:01:18

Since

We get that

Now we also know

And manipulation of that reveals

So we can reword equation 2 and obtain

Which means this rotating pattern...

...works for strange cases of roots.

Example:

#9 Re: Introductions » ɑβγ » 2014-09-03 02:44:55

Hello ganesh, ShivamS, and anonimnystefy.

Reality is the acceptance of anything, because if you can't accept the fact that anything is reality, you won't realize that reality is the acceptance of anything.
(The topic gets confusing fast...)

My favorite Greek letter would have to be


(Capital Delta)

#10 Re: Euler Avenue » Area by Integration » 2014-09-02 09:23:14

You can't really use a magical formula to obtain the answer easy peasy because you have 3 functions, each with their own graph.  Since I don't know how the graphs are oriented and how they intersect, the only actual answer without anymore information would be the sum of the negative or positive of each integral of each function, i.e.:

That's the most precise answer (in reduced form) that can be obtained without further information.

#11 Re: Introductions » ɑβγ » 2014-09-02 08:33:01

Hi bobbym and Agnishom!

Info about me:

Age: 14
Hobby: Theoretical Mathematics (duh...)
Gender: Male
Favorite Area in Math: Integral calculus
Favorite Color: Blue
Least Favorite Area in Math: Anything applied to reality, except for theoretical reality, even if the theoretical reality is based off of reality.
NOTE: I love paradoxes.

#12 This is Cool » i = i^x mod 4 » 2014-09-02 07:13:37

αβγ
Replies: 10

This is really weird:


for x>0 and x is positive.

If this works for

, then it should work for other imaginary values.... (i.e. imaginary numbers created other ways, but still using a radical)

#13 Introductions » ɑβγ » 2014-09-02 06:52:41

αβγ
Replies: 13

Hi! My name is ɑβγ, I'm 14 (turning 15 soon) and I love all things math! (Except applied math, I just like the theoretical stuff...)
Also I love solving theoretical problems, not the applied ones like "If I have 3 apples, what is the integral of apples if the interval is 0 to the number of apples I have and the integrand is also the number of apples I have?"

P.S The answer is 9 if you're wondering... Since

Anyways, HI!!!

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