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What is meaning of imaginary exponent e.g. $a^i$?

e.g. $a^b$ can be expressed as $a*a*a ...$ (b times)

how $a^i$ can be interpret ? Is it possible that $a^i$ is real number ? I am not able to understand why following hold true even if it has imaginary exponent

Euler's identity $ e^{i\pi} = -1$

Is there any document to explain arithmetic for imaginary exponents e.g. How to expand ${(a+b)^i}$

Kalpesh Chavan
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  • Possible duplicate of https://math.stackexchange.com/questions/9770/understanding-imaginary-exponents?rq=1. – Matteo Feb 09 '22 at 09:20
  • I agreed there are certain rules like fraction mean root (any nth) and negative mean inverse. I am not talking here fractional/negative exponents – Kalpesh Chavan Feb 09 '22 at 09:37

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