>even roots of negative numbers are complex
but what about odd roots? or fractional roots? it is not obvious to me at all.
and thinking about this anons examples: >>11129565
yes i see that (-1)^0.5 = i
and so (-0.5)^(-0.5) is complex as well.
but what about x=-1/3 for example.
(-1/3)^(-1/3) why is it complex? not obvious at all. also what if x is a negative integer. for example (-2)^(-2) = 0.25 so why is x^x not defined for negative integers?

also check this out, google
(-0.5)^(-0.5) then 1/((-0.5)^(0.5))
both are complex
- 1.41421356 i

now google (-0.2)^(-0.2) and get
1.11622474 - 0.810984747 i
but 1/((-0.2)^(0.2)) is suddenly real
-1.37972966146
and google calc doesn't seem to support taking non-square radicals.
but desmos thinks that (-0.2)^(-0.2) is real.

also (-3)^(-3) is perfectly real, but
(-3.001)^(-3.001) is complex.
this is mind boggling
What book should I read to learn more about this? I've check 1000 textbooks and none of them cover this.