How to find $\Gamma(i)$?

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using the basic definition that $\Gamma(n)=\int_0^{\infty}e^{-x}x^{n-1}dx$
It would not be easy to find $\Gamma(i)$ then what method must be used to calculate it and would the result be real or complex?
Please Explain$_\cdots$

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One approach: The integral converges for $\Gamma (1+i)$. Then, use the recursive relation to render $\Gamma (1+i) = i \Gamma (i)$.