The discussion revolves around the properties of complex exponentials, specifically the expression e^(i*2pi*1/15) and its relationship to the expression (e^(i*2pi))^(1/15). Participants are questioning the validity of applying the exponentiation rule (A^(b))^c = A^(bc) in the context of complex numbers.
The discussion is ongoing, with participants providing insights into the limitations of exponentiation rules for complex numbers. Some guidance has been offered regarding the safety of using integer powers, but there is still uncertainty about the general case.
Participants note that the application of exponentiation rules may differ based on the nature of the base and the exponents involved, particularly when dealing with complex numbers.
kougou said: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 said:Because it isn't. The rule (A^b)^c=A^(bc) doesn't hold for complex exponents. As your example shows.
kougou said:But why?
When I use take the positive integer power of complex exponential, it works. What's the rule?