Raising Complex Numbers to Powers of Angles - What Happens?

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Raising a complex number to the power of an angle in radians involves using the exponential function and logarithms. Specifically, for the complex number i raised to an angle a, the formula is (i)^a = e^(a x log(i)). The logarithm of i is calculated as log(i) = i x π/2, leading to the expression (i)^a = e^(i x aπ). This indicates that the result is another complex number, demonstrating that the behavior of complex numbers in this context is more straightforward than that of real numbers raised to an angle. Understanding these principles can clarify the relationship between complex exponentiation and angles.
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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?
 
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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 ?
 
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...
 
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