
1 to an exponent
I have two questions:
1) Say I want to find solutions to $\displaystyle (1)^{m/n} $ for integers m and n. When does a real solution exist to this? And when do only complex solutions exist?
2) Say x is an irrational number. What is $\displaystyle (1)^x $?

1) Real solutions will exist if n is odd. Else imaginary.
See it's simple. (1)^(m/n) is merely {(1)^(1/n)}^m
It's the mth power of the nth root of 1.

2) I'll try using Demoivre's theorem here.
1= e^{i( pi)} where i is the square root of 1 and pi iswell, pi :P
so (1)^x = e^{i(pi)x} ???