kep

what do u think about this
in complex numbers {(-1)^0.5 = i}
-1=-1

(-1)^0.5 = (-1)^0.5

(1/-1)^0.5 = (-1)^0.5

{(1)^0.5}/{(-1)^0.5} = {(-1)^0.5}/{(1)^0.5}

(1)^0.5 * (1)^0.5 = (-1)^0.5 *(-1)^0.5

1= -1

this is one of fallacy in complex numbers
so what is the wrong step?

Pommie

1/(-1^½) != -1^½

Mike.

Papabravo

What is wrong is that in the second line you assumed that i was equal to 1/i and that is not true. The algebra of complex numbers is different than the algebra of real numbers. That is why we use a different symbol so that we won't be tempted to make inconsistent assertions like that one. The problem with your original assertion is that when combining real numbers and complex numbers the order of operations is important AND many of those operations are NOT commutative.

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kep

thanx
got da idea 1/i != i
i miss da basics !!!!

3iMaJ

1/i = -i

Close though.

3iMaJ

The algebra of complex numbers is the same as the algebra for real numbers, one just has to be careful. The same rules apply. However, the calculus of complex numbers does get a little tricky. Order of operations is always important, there aren't times that you can just "forget" about them whether you're working with real, rational, complex, whole, or whatever type of number system you dream up. Although if you make one up, you're going to have to prove associtivity, transitive, communitivity etc.

Papabravo

In order to substantiate the claim that the two algebras are the same you need to start with elements of the set which are different. Now it is true that the algebra of real numbers is contained within the algebra of complex numbers. It is the set of all complex numbers with the inaginary part set equal to zero. There is a much closer relationsip between vector algebra and complex algerbra.

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3iMaJ

I made no such claim. I only said there certain rules that numbering systems follow. Yes the real numbers are a subset of the complex numbers, but that in no way implies that there are two different kinds of algebra?

And a side note, real numbers can be just as easily be manipulated using vector algebra as complex numbers, although they typically aren't because there is no reason to complicate it to such a degree.

In the end its all algebra, all following the same rules.

43617373

How is a number being obtained from a negative in the square root, or am I forgetting a large part of my algebra.

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dknguyen

You break up the number underneath the square root:

sqr(-x) = sqr(-1)*xqr(x)

and then replace the sqr(-1) with i, making the result an imaginary number (or more specifically, a complex number with a real component of zero, at least for this example). It's the basis for math with complex numbers. Maybe you just never learned it?

Papabravo

I invite the other members to reread your original post to see if you made precisely that claim. It sure sounds like you did to me, but what do I know, I'm just a graduate engineer.

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Nigel Goodwin

My daughters doing A level Further Maths, and apparently you need to be 'weird' to be any good at it - she fits right in!

According to the teachers, A level Further Maths is more difficult than a normal maths degree, and where top universities require applicants to have grade A's in their subjects, even a grade E is acceptable if it's Further Maths.

Needless to say, I haven't got the faintest clue what she's doing with it! - means she can't ask me to help

I did offer to help if she took Physics, but she took Chemistry, Maths, Further Maths and Music Technology - so I'm safe!

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quixotron

Further maths??

The 500 and 600 level math courses at Purdue require advisor consent or a minimum grade of B or better. A is the highest you can get on a 4.0 scale, never heard of an E or and "S". 700 level math courses require PHD status or consent of an advisor with superb background mathematical skills.

The highest I have taken is random variables and electromagnetics field theory, both 600 level courses. I got a B in both, they were rough courses, designed to select phd and research assistants, it dropped my gpa a bit though. If I ever take something like that again, it'd be two classes only.

Nigel Goodwin

An A Level course in the UK (notice my location is filled in, so you know where I am), it's considerably above normal A Level maths courses.

Interesting TV phone in the other day, apparently Maths degree courses have the highest drop out rate of any courses? - and a university maths lecturer rang in to say that it's mostly only the Further Maths students who can cope with the degree course?.

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DMW

How about:

' = reoccurring

X = 0.9999' [* 10]
10X = 9.9999' [-X]
9X = 9.0 [/9]
x = 1