I have two questions:

1) Say I want to find solutions to 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 ?

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- August 19th 2009, 09:24 AMJG89-1 to an exponent
I have two questions:

1) Say I want to find solutions to 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 ? - August 19th 2009, 09:29 AMbandedkrait
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.** - August 19th 2009, 09:36 AMbandedkrait
2) I'll try using Demoivre's theorem here.

-1= e^{i( pi)} where i is the square root of -1 and pi is-well, pi :-P

so (-1)^x = e^{i(pi)x} ???