
Pursuing knowledge
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 TI89 and got i. This would be great, except I can't get the algebra to do that.
x=1/i
x^2=1/(i^2)
x^2=1/(1)
x^2=1
x=sqr(1)
x=i
i!=i, so I decided to try it with 2/i
x=2/i
x^2=4/(i^2)
x^2=4/1
x^2=4
x=sqr(4)
x=sqr(1*4)
x=2 * sqr(1)
x=2i
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 TI89 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; 04122003 at 04:36 PM.
Away.

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
becomes
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; 04122003 at 06:46 PM.

Pursuing knowledge
Thank you, I feel dumb now As I said, the TI89 knows all...

Programming SexGod
no need to square at all, just rationalize
1/i
Multiply by i / i
i/(1)
which is
i
Last edited by Polymorphic OOP; 04122003 at 08:23 PM.
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