URGEN taking the power of complex exponential

[kougou]

Homework Statement

e^(i*2pi*1/15) is equal to ( e^(i*2pi) )^(1/15) = (1)^(1/15)=1

Why this is false?

Homework Equations

((A)^(b))^c=A^(b*c)=A^(bc). Why this isn't the case for complex exponential?

The Attempt at a Solution

 

[Dick]

Homework Statement

e^(i*2pi*1/15) is equal to ( e^(i*2pi) )^(1/15) = (1)^(1/15)=1

Why this is false?

Homework Equations

((A)^(b))^c=A^(b*c)=A^(bc). Why this isn't the case for complex exponential?

The Attempt at a Solution

Because it isn't. The rule (A^b)^c=A^(bc) doesn't hold for complex exponents. As your example shows.

 

[kougou]

Because it isn't. The rule (A^b)^c=A^(bc) doesn't hold for complex exponents. As your example shows.

But why?
When I use take the positive integer power of complex exponential, it works. What's the rule?

 

[Dick]

But why?
When I use take the positive integer power of complex exponential, it works. What's the rule?

If b and c are integers you should be safe. If A is a positive real and one of b or c is an integer, that should also be ok. Otherwise, I think it's dangerous.