aye aye
If i is the usual unit imaginary number (Sqrt(-1)), what is i^i ?
Labels: mathschallenge, SharedPuzzle
posted by Chris at
10:57 AM
Sunday, August 16, 2009
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8 Comments:
-1 methinks
whoops no...err....ummmm....
More negative than -1
Anonymous 1: No.
Anonymous 2: No, no, no and no.
Anonymous 3: No.
lets pick 0.2078.....
Any other Form would give too many hints, don't wanna destroy Chris' problem again =)
e^(-pi/2)
i agree with "tha b:::.:::H" as he is correct :P
That was quick. At least I made a few heads hurt.
i = e^( i pi/2 + i 2 pi N) where N is any integer (inc -ve values)
=> i^i = e^(-pi/2 - 2 pi N)
N = 0 => principal value (i^i) = e^(-pi/2) = 0.20788...
All the solutions are real and there are infinitely many of them.
Here are a few more values:
7.24947*10^-7, 0.000388203, 111.318, 59609.7
I bet there's some science out there that needs this result.
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