Re: x^x = 1/4

Keith F. Lynch wrote:
>> If you're speaking of the change of sign of the imaginary, that's
>> meaningless. Any solution to x^x equals a real number has another
>> solution with the opposite sign on the imaginary, i.e. the complex
>> conjugate.
>

Quasi wrote:
>> Is this obvious?
>> Even if it is, can you explain it a little?
>

Keith F. Lynch wrote:
>> I have a simpler explanation than the other two people who answered you.
>>
>> There is absolutely nothing that distinguishes i from -i. They're
>> not equal to each other, but in any valid equation whatsoever, if
>> you replace every i with -i and vice versa, it will still be valid.
>

Quasi wrote:
> It may be simpler, but I don't buy this explanation, sorry.
>
> To say that when an equation has z as a solution then it also has
> conjugate(z) as a solution, implies that the one solution induces a
> second. That's not immediate from the indistinguishability of i and
> -i. It really depends on the form of the equation.

I'm certainly no expert, but surely (-i)^(-i) is not the same as i^i,
is it?

.

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