Complex Power Operation: Is x^iy Possible?

[scientificon]

I am wondering whether complex power operation is valid.

For example, can 2ⁱ³ be calculated? Or is it undefined?

Thanks

 

[pwsnafu]

Yes. See Euler's formula.

 

[Fredrik]

See the FAQ post about this topic.
https://www.physicsforums.com/showthread.php?t=637214 .

 

[lurflurf]

complex exponentiation is defined by

x^y:=e^(y log(x))