- 13 Mar '04 21:52This is for those math people who love complex space:

i think it is very difficult to conceptualize it, but i^i is actually a real number and is very easy to find using Euler's Formula:

exp(i*Pi) = -1 = i^2

=> i^i = exp(-Pi/2) = 0.207879......

i think this is fascinating and would like to be able to understand why this is so....can any of you give me a geometric or any other reason why i^i should be a real number?

thanks - 14 Mar '04 02:50

i knew this also, but haven't seen the proof as to why.*Originally posted by davegage***This is for those math people who love complex space:**

i think it is very difficult to conceptualize it, but i^i is actually a real number and is very easy to find using Euler's Formula:

exp(i*Pi) = -1 = i^2

=> i^i = exp(-Pi/2) = 0.207879......

it is logical, though, since*i*is such an unusual quantity.

hope soemone else can help us here. - 14 Mar '04 18:15

Is it because raising a number to an imaginary power rotates it in the complex plane? Raising i to an imaginary power looks like it rotates i exactly onto the real plane.*Originally posted by davegage***This is for those math people who love complex space:**

i think it is very difficult to conceptualize it, but i^i is actually a real number and is very easy to find using Euler's Formula:

exp(i*Pi) = -1 = i^2

=> i^i = exp(-Pi/2) = 0.207879......

i think this is fascinating and would like to be able to understand why this is so....can any of you give me a geometric or any other reason why i^i should be a real number?

thanks