On Jul 25, 9:28 am, Hongyi Zhao <hongyi.z...@gmail.com> wrote: > Hi all, > > What's the geometry meaning of i^i ? Here, i is the imaginary unit. > > Regards > -- > .: Hongyi Zhao [ hongyi.zhao AT gmail.com ] Free as in Freedom :.
i^i is not an imaginary number or numbers, but a set of equally spaced real numbers.
Just as product of two negative numbers returns positive,exponentiation of pure imaginary numbers returns as pure real number.
From Euler's identity the set is seen to be odd multiples of pi/2, (4*k + 1)pi/2. Geometrically seen on the Argand diagram they are all on the real axis, say formed by a point of a rolling circle 2 units radius rolling on real axis. i.e., (.., -7,-3,1,5,9, ..)* pi/2.