What is a number raised to an imaginary power?

[Radarithm]

Homework Statement

How would you define a number that is raised to an imaginary power?

Homework Equations

λⁱ= ?
λ = 6+4i

The Attempt at a Solution

e^{ln x} = x
Other than that I have absolutely no idea how to go about solving this.

 

[DrClaude]

There is a FAQ on the subject: https://www.physicsforums.com/showthread.php?t=637214

 

[Radarithm]

There is a FAQ on the subject: https://www.physicsforums.com/showthread.php?t=637214

Thanks for pointing that out.