i

[itolduso]

i^2 = -1
i = ?
sqrt(-1) = ?

[brightsky]

i = sqrt(-1)

[m@tty]

[itolduso]

what is ln(-1)/pi?

[TrueTears]

i


it's just definitions

[m@tty]

what is ln(-1)/pi?

Oh and realise that this is all imaginary, hence, don't expect to have a conceptual understanding of i or expect to be able to visualise where it would be on a number line...

[itolduso]

i


it's just definitions

What definition are you referring to?

[TrueTears]

sqrt(-1) = i

in fact the proper definition is i^2 = -1 and sqrt(-1) = i is a consequence

[itolduso]

I havent seen such a definition. Where can i find it?
sqrt(-1) = i,
.: ln(-1)/pi = e^(ipi/2)?

[Martoman]

what is ln(-1)/pi?

Oh and realise that this is all imaginary, hence, don't expect to have a conceptual understanding of i or expect to be able to visualise where it would be on a number line...

I see it on a number line as hovering above it. It adds a dimention to numbers.

[brightsky]

I havent seen such a definition. Where can i find it?
sqrt(-1) = i,
.: ln(-1)/pi = e^(ipi/2)?

Well it so happens that . Hence plugging in, you get .

And just as m@tty has done above, do some manipulation of this:

[m@tty]

what is ln(-1)/pi?

Oh and realise that this is all imaginary, hence, don't expect to have a conceptual understanding of i or expect to be able to visualise where it would be on a number line...

I see it on a number line as hovering above it. It adds a dimention to numbers.

Yeah, so its not on the number line. It is separate, a new concept, part of the unknown...

On an Argand diagram you just treat it like you do the vertical axis on the Cartesian plane

[TrueTears]

what is ln(-1)/pi?

Oh and realise that this is all imaginary, hence, don't expect to have a conceptual understanding of i or expect to be able to visualise where it would be on a number line...

I see it on a number line as hovering above it. It adds a dimention to numbers.

yeah there actually IS a number line for complex numbers (check the wiki link below), in fact our real number line can not represent i, so i is kinda like the imaginary unit for the complex number system, you can think of it as the complex equivalent of a real number line.

I havent seen such a definition. Where can i find it?
sqrt(-1) = i,
.: ln(-1)/pi = e^(ipi/2)?

i dono, elementary algebra textbooks? or just read here

http://en.wikipedia.org/wiki/Imaginary_unit

i forgot the mathematician who formally defined i, maybe it says somewhere in the wiki article.

[kyzoo]

what is ln(-1)/pi?

Oh and realise that this is all imaginary, hence, don't expect to have a conceptual understanding of i or expect to be able to visualise where it would be on a number line...

I see it on a number line as hovering above it. It adds a dimention to numbers.

Wait a minute...if "i" adds a 2nd dimension to the numbers, then that means there's a 3rd dimenion, and a 4th, and so on?

[Martoman]

In a sense it adds a a certain dimentionality to them yes.