Is the Complex Number Identity True for Imaginary Numbers and Integer Powers?

[zetafunction]

let be n and integer and 'i' the imaginary unit

is then true that $$n^{ \frac{2i\pi n}{log}} =1$$

i believe that is true

 

[AndyJohnD]

let be n and integer and 'i' the imaginary unit

is then true that $$n^{ \frac{2i\pi n}{log}} =1$$

i believe that is true

new to this forum
and newish to complex numbers
could you explain what (2ipin)/log is?
ie what is something/log
It may be that I am unfamiliar with the notation
thanks

 

[mathman]

log by itself is meaningless. You need log(something).

 

[AndyJohnD]

thanks
I thought I would try and prove the identity but then got stuck on log of thin air

 

[alexfloo]

http://en.wikipedia.org/wiki/Root_of_unity

This article should give you some insight.