🚀 go-pugleaf

In article <5gndo3$5u7@flounder.trans.ge.com>, Ron Bauerle
<bauerle@erie.ge.com> writes
>In article <5gk8lm$qmj@opus.vcn.bc.ca>, landmark@vcn.bc.ca (Scott Phung) writes:
>>Martin Ward <martin@ward-hull.demon.co.uk> wrote:
>
>>MW> Some are not unique.  I have presented all the possibilities but I think
>>MW> we should accept the canceled form as the day, so i^i Day is 1 May
>>MW> rather than 2 October.  The latter could be (i^i Day)'.
>>
>>Isn't it ironic how the imaginary number raised to the imaginary
>>power equals a real number? (Involving the important constants pi,
>>and e)  :-)
>
>Anybody got a proof for that?  i^i = exp(-pi/2)?
>
>Thanks,
>
>Ron Bauerle
>
By De Moivre's theorem    e^(i*pi/2) = cos(pi/2) + i*sin(pi/2)
                                     =     0     + i*1
                                     =     i

                        so      i^i  =   (e^(i*pi/2))^i
                                     =   e^(i*i*pi/2)
                                     =   e^(-pi/2)
-- 

Martin Ward

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"When *I* use a word", Humpty Dumpty said in rather a scornful tone, "it
 means just what I choose it to mean - neither more nor less".
"The question is", said Alice, "whether you *can* make words mean so many
 different things".
"The question is", said Humpty-Dumpty, "which is to be master - that's all".

"Through the Looking-Glass" - Lewis Carroll.
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