I wanted to know what $x$ is in this equation: $x! = i$.
I tried using normal calculators which just gave a math error, tried searching google which was pretty useless, zero results, and last but not least tried using Wolfram, which gave an answer
(which gave 1 answer on pc but gave 3 on an Android device???)
but wolfram's answer provided a transcendental number(the answer) without giving its fractional form, so my questions are
Note $i$ here is the imaginary unit not a variable
What is $x! = i$ in fractional form; How did you get the answer?
The usual notation of $x!$ only covers real numbers. We extend it using the Gamma Function defined as: $$\Gamma(z)=(z-1)! \text{ for $z\in\Bbb Z^+$}$$ $$\Gamma(z)=\int_0^{\infty}{t^{z-1}e^{-t}dt} \text{ otherwise}$$
You'll need to use the second definition to find the answer to your problem, specifically find $$\Gamma(x+1)=i$$
Therefore we are solving: $$\int_0^{\infty}{t^xe^{-t}dt}=i$$