Reciprical of i
i is defined as the square root of -1, (sqr(-1) or (-1)^(.5) )
A friend just asked me what 1/i is, so I punched it into the TI-89 and got -i. This would be great, except I can't get the algebra to do that.
i!=-i, so I decided to try it with 2/i
x=2 * sqr(-1)
Same result...I tried again for 3 and ended up with 3i. I don't see any errors in my algebra, but as far as I know, the TI-89 is infallible. I once saw it described as "a massive beast of knowledge" on these boards, and I agree. Would someone please enlighten me as to the nature of my error?
Last edited by confuted; 04-12-2003 at 05:36 PM.
The Earth is not flat.
When you solve for a square root you get two answers plus and minus hence:
x = 1/i
x^2 = 1/(i^2)
x^2 = 1/(-1)
x^2 = -1
x = +/- sqr(-1)
x = +/- i
Since x cannot be +i:
1/i = i
1 = i^2
1 = -1 ..... bzzzt
it must be - i:
1/i = -i
1 = i * -i
1 = -(i*i)
1 = -(-1)
1 = 1
Last edited by Clyde; 04-12-2003 at 07:46 PM.
Thank you, I feel dumb now As I said, the TI-89 knows all...
no need to square at all, just rationalize
Multiply by i / i
Last edited by Polymorphic OOP; 04-12-2003 at 09:23 PM.