What is a number raised to an imaginary power?

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A number raised to an imaginary power can be defined using Euler's formula, which relates complex exponentials to trigonometric functions. The discussion centers around the expression λi for λ = 6 + 4i, highlighting the challenge of solving it. Participants reference a FAQ that provides additional insights into the topic. The use of the natural logarithm is mentioned as a potential approach, but clarity on the solution remains elusive. Understanding the concept of imaginary exponents is crucial for further exploration in complex analysis.
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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


eln x = x
Other than that I have absolutely no idea how to go about solving this.
 
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There is a FAQ on the subject: https://www.physicsforums.com/showthread.php?t=637214
 
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DrClaude said:
There is a FAQ on the subject: https://www.physicsforums.com/showthread.php?t=637214
Thanks for pointing that out.
 
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