This is for those of you that learned imaginary numbers
Note: roots are written as to the power of a fraction, due to the lack of square root sign
i = -1^1/2
Yes, that's what i is, let's creat the paradox!
i² = -1
i⁴ = 1
i = 1^1/4
i = + or - 1
So is i real or not?
Help!!!

Categories: Math [t]

Uh..... I haven't learned about imaginary numbers yet. Sorry.
» randomjunk on 2006-12-01 09:11:57

hmm.
Well, if you say that x=-1 and then you say that x^4=1 then you could say that x=1^1/4 and that x=+/-1. But x doesn't equal 1, it equals 1, because that's the way you defined it. Once you define x it can't become a variable again. If x hadn't been defined yet, you would still know that x can't equal both +1 and -1, it's one or the other. So you have to do something else to figure out which is right (usually by deciding which makes sense in context). Obviously in this case you already know.
It would be most correct to say, "x=1^1/4", thus
x=1 or -1 or -1^1/2 or -(-1^1/2). The last possibilities are usually left out because a common assumption is that we're only dealing with real numbers. Often times they do state that assumption at the beginning of the problem, but not always. In the case of i, you know which one of the four that i is actually equal to, because it's already been defined.

I like your background, by the way. :D
» Zanzibar on 2006-12-01 09:33:28

I have no idea...
Um...yeah, what he said. XD Sorry I couldn't help.
» Silver-dot- on 2006-12-01 11:00:31

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