Raising Complex Numbers to Powers of Angles - What Happens?

[Andrea2]

is there anyone who can tell me what happen when i raise a complex number to the power of an angle in rad? for example, what is the result of (i)^1rad?

 

[JJacquelin]

is there anyone who can tell me what happen when i raise a complex number to the power of an angle in rad? for example, what is the result of (i)^1rad?

Since you ask about the power of a COMPLEX number, so I suppose that you already know what happen when you raise a REAL number to the power of an angle in rad. For example, what is the result of 2^1rad ?

 

[Andrea2]

i don't know exactly what happen if i raise a real number to the power of an angle, i tried to answer also to this question, but five minutes ago i think I've found the answer to my first question, and i think that this problem is more difficult with real numbers than with complex! My solution is that (i)^a = e^(a x log(i)) with a=angle in rad. log(i) = i x p/2 (p=3.1416...), so (i)^a = e^(i x ap), that is a complex number...