Hmmm... (1 Viewer)

[Veck]

i divided by -1 is obviously (- i) correct?

hmm.. if
i = root(-1)
= (-1)^1/2

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

so... 1 / i = (- i) ???

how does this work..
hmm.. just a thought.

 

[withoutaface]

1/i=1/i*i/i=i/(-1)=-i

I don't see what you're getting at....

 

[gordo]

just 'rationalise' the bottom dude

 

[Veck]

haha yeah I know, I just thought it slightly weird that the minus of something could equal its reciprocal..

stupid, but yeah.. hahahhaah
sorry for wasting all of your time

 

[gordo]

its like the normal
if your tangent gradient is -i
then your normal gradient is 1/i, cause they are 90 degrees apart
since i is on the argand diagram, every time u multiply by i, you are rotating it 90 degrees anticlockwise

 

[Slidey]

It just follows the general rule.
All positive powers of i 0mod4 give you 1.
All positive powers of i 1mod4 give you i.
All positive powers of i 2mod4 give you -1.
All positive powers of i 3mod4 give you -i.

Of course, you have to stop and think, because you're now going backwards, but when you have i^4 and you take one from the power you get i^3=-i, so if you have i^0 and you take one from the power, you get i^-1=-i.