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docnet

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- Is it possible to exponentiate a number that is not e to a complex number?

Does it make sense to write ##r^c##

where ## r\in R/e ## and ##c\in C## ?

where ## r\in R/e ## and ##c\in C## ?

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- Thread starter docnet
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- #1

docnet

- 587

- 242

- TL;DR Summary
- Is it possible to exponentiate a number that is not e to a complex number?

Does it make sense to write ##r^c##

where ## r\in R/e ## and ##c\in C## ?

where ## r\in R/e ## and ##c\in C## ?

- #2

FactChecker

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- #3

mfb

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Both r and c can be complex here. As a notable example, ##i^i = e^{i \log{i}} = e^{i (\frac{\pi}{2} i)} = e^{- \frac{\pi}{2}}## which is real.

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