What is a number raised to an imaginary power?

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SUMMARY

A number raised to an imaginary power can be defined using Euler's formula, which states that e^(ix) = cos(x) + i*sin(x). In the discussion, the specific example of λ = 6 + 4i is presented, where λi can be evaluated using the properties of complex exponentiation. The user expresses confusion about the solution process but acknowledges the existence of a relevant FAQ for further guidance.

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Radarithm
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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.
 
Last edited:
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There is a FAQ on the subject: https://www.physicsforums.com/showthread.php?t=637214
 
Last edited by a moderator:
DrClaude said:
There is a FAQ on the subject: https://www.physicsforums.com/showthread.php?t=637214
Thanks for pointing that out.
 
Last edited by a moderator:

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