What is i?

i only has one property that is relative to the real numbers, that is i^2=-1

btw new people may get tricked by my example so i^2=-1 is definately better than i=sqrt(-1)

Quote:

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Originally posted by bugzpodder
i only has one property that is relative to the real numbers, that is i^2=-1

btw new people may get tricked by my example so i^2=-1 is definately better than i=sqrt(-1)

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Well, I can't disagree with that!
:D

Except,

"new people"?
How New?

:p

anyone who doesn't know the example lol.

Quote:

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Originally posted by NotLKH

Again, you are confusing dimensions with that which is contained in an array.

Now, talk about an impossibility!

How do you Dim an array, where its X Ubound is 5i Apples, and its Y Ubound is 5i Apples?
Or even, where Arr(X,Y) has an Ubound of its X = 5I, and the same for Y?


How,How,How,How,How,How,How,?????
:(

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Who said we were programming? I can have an array of saucers on a table if I wanted to!

Uhm...

(-1)^(1/2)=i

because (-1)^(1/2) is the sqrt(-1) which is i.

and...

i^2 = -1

and i^3 = -i

and i^4 = 1

and... whatever....

all i really is, is just a nice way to write sqrt(-1)

because replace sqrt(-1) with an i and you get the same result

so i = sqrt(-1)

and since it's always best to show equality with the varible alone, i = sqrt(-1) would be technically the best

sqrt(-1)*sqrt(-1) = -1
just like
sqrt(2)*sqrt(2)=2

and .999.... <> 1

duh.

1)

Quote:

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and .999....<>1
duh

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Why??

2) For everyone that doesn't know, a very useful HTML tag is the superscript- good for powers.
e.g:
i [ s u p ] 2 [ / s u p ] (without the spaces)
= i²

Also subscript - good for Chemistry.

H [ s u b ] 2 [ / s u b ] (without the spaces)
= H₂

Quote:

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Originally posted by DiGiTaIErRoR
all i really is, is just a nice way to write sqrt(-1)

because replace sqrt(-1) with an i and you get the same result

so i = sqrt(-1)

and since it's always best to show equality with the varible alone, i = sqrt(-1) would be technically the best

sqrt(-1)*sqrt(-1) = -1
just like
sqrt(2)*sqrt(2)=2

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also, sqrt(2)*sqrt(2)=sqrt(2*2)=sqrt(4)=2

but, sqrt(-1)*sqrt(-1)=sqrt(1)=1

i=sqrt(-1) isn't any good PRECISELY BECAUSE OF THIS!

Quote:

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Originally posted by bugzpodder
also, sqrt(2)*sqrt(2)=sqrt(2*2)=sqrt(4)=2

but, sqrt(-1)*sqrt(-1)=sqrt(1)=1

i=sqrt(-1) isn't any good PRECISELY BECAUSE OF THIS!

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I just noticed, the error comes about from useing the sqrt(-1) as
a proper function, but since sqrt(-1) cannot be evaluated thru the
normal properties of sqrt, then the associated properties of the sqrt function cannot be relied upon. So, trying to do a proof useing sqrt(-1) will produce imprecisions similar to that when we've seen division by zero in proofs.

So, My Suggestion, lets define the rule of priority, no Matter What,
Once you see sqr(-n), you MUST substitute i*Sqr(n), before you
do anything else.



;)

Hmm, I would have to say that i is implicitly defined as i² = -1, because of what Bugz said. I don't think i can be explicitly defined accurately...

i agree with you guys. new people who does not know this may follow exactly what I did if they were given i=sqrt(-1)... (not saying that they will every time but there is a chance that they might)

Quote:

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Originally posted by NotLKH
So, My Suggestion, lets define the rule of priority, no Matter What,
Once you see sqr(-n), you MUST substitute i*Sqr(n), before you
do anything else.

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Edits (hereinafter) are in Bold

I was taught to use i more like a variable, and that Sqrt(-n) [where n is positive] should be rewritten with Sqrt(n×i²) which allows you to square rooting it easier, since the power of half will cancel the power of two.

Are there any limitations or problems doing it the way I do? A lot of the stuff I post on here which I learnt from school seems to have a talent of being wrong.

if you are taught in school its most likely right than wrong. but there are a few things your teacher may not know (that goes with experience rather than teaching skills) that happens we are all human but i just want to stress again that its most likely right than wrong.

Well, it's kinda like in Chemistry where they deliberately teach you wrong as to not confuse you, like electron configurations.

First of all they say the e.c. of Na is (2, 8, 1) then later they tell you that it's wrong and to write it as (1s² 2s² 1p⁶ 3s¹) or something... I can't exactly remember.

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sqrt(2)*sqrt(2)=sqrt(2*2)=sqrt(4)=2

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Actually:
sqrt(2)*sqrt(2)=sqrt(2*2)=sqrt(4)=+/-2

So, you could sort of say, using this, that sqrt(2) -real number- squared can give a negative number (-2). Which is wrong
=> This logic is not really valid. (At least, after reading it for 10 min. it is not. Maybe after longer i might have changed my mind. Just a thought)

yea thats why sqrt(4) is defined to be the principal square root which is 2. however it isn't a reason that you do not acknoledge the other square root with is -2, since (-2)*(-2)=4

plus the domain of sqrt(x) defines x to be a real >=0 so technically you can't even put sqrt(-1) because of the definition

I was intrigued by Notlkh's signature and hence..........

Now, my exposure is to Math is limited to High School and what little I ahve picked up along the way later, and no way do I claim myself an authority:o

That said, my two paise...........

Assumptions:
1) A Definition can be only one of two: It has to be constructed arbitarily from one's whim and fancy OR inducted/deducted from an already established definition or observation.
2) Mathematical proof is solely dependent on consistency within the given framework.

Code:

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Definitions:
1: {Arbitary} i is point on the real plane such
that it is a distance y, 90 degrees from the point x.

Further, x is identified with the point (0,0) and y with point (0,1)

2: {Derived from an existing entity viz. POWER} The nth root of A
is that which when raised to power n results in A.

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Axioms:

Code:

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1) In a plane; (x,y) * (u,v) = (xu - yv, xv + yu)

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Using Definition One:
i = (0,1)

Using Axiom One:
i * i = (0,1) * (0,1) = (-1, 0)

Ergo: i ² = -1

Using Definition Two on the above result
n = 2 ; A = -1, ergo: Square Root of -1 = i

QED

Neither of the definitions I have proposed are wrong. Therefore, the above proof(s) are admissable, given my assumptions. As to their being right, I'll look forward to your bouquets and brickbats.:)