Re: x^x = 1/4

On 8 Jan 2006 23:54:17 -0500, "Keith F. Lynch" <kfl@xxxxxxxxxxxxxx>
wrote:

>Gib Bogle <bogle@xxxxxxxxxxxxxxxxxxxxxxxx> wrote:
>> john wrote:
>>> Easily done. here is a list, also from MathCad, for x^x = a,
>>> 0.2 <= a <= 0.9
>
>>> 0.2 -0.0111293901917468-1.01739249615655i
>>> 0.3 0.107262163062439+0.821526901788799i
>>> 0.4 0.193822522073504+0.656549581040713i
>>> 0.5 0.262892828009026+0.499669435669579i
>>> 0.6 0.320971270023043+0.327577921754899i
>>> 0.7 0.462337531535098
>>> 0.8 0.739533650012175
>>> 0.9 0.888135328827093
>
>>> john
>
>> The behaviour after a = 0.3 is smooth, but the jump from 0.2 to 0.3 is
>> pretty dramatic, ...
>
>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.

Is this obvious?

Even if it is, can you explain it a little?

quasi
.

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